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38
doc/complex/complex-tr1.qbk
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@ -16,12 +16,12 @@ Although there are deceptively simple formulae available for all of these functi
implementation that used these formulae would fail catastrophically for some input
values. The Boost versions of these functions have been implemented using the methodology
described in "Implementing the Complex Arcsine and Arccosine Functions Using Exception Handling"
by T. E. Hull Thomas F. Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software,
by T. E. Hull Thomas F. Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software,
Vol. 23, No. 3, September 1997. This means that the functions are well defined over the entire
complex number range, and produce accurate values even at the extremes of that range, where as a naive
formula would cause overflow or underflow to occur during the calculation, even though the result is
actually a representable value. The maximum theoretical relative error for all of these functions
is less than 9.5[epsilon] for every machine-representable point in the complex plane. Please refer to
formula would cause overflow or underflow to occur during the calculation, even though the result is
actually a representable value. The maximum theoretical relative error for all of these functions
is less than 9.5[epsilon] for every machine-representable point in the complex plane. Please refer to
comments in the header files themselves and to the above mentioned paper for more information
on the implementation methodology.
@ -35,9 +35,9 @@ on the implementation methodology.
[h4 Synopsis:]
template<class T>
template<class T>
std::complex<T> asin(const std::complex<T>& z);
__effects returns the inverse sine of the complex number z.
__formula [$../images/asin.png]
@ -52,9 +52,9 @@ __formula [$../images/asin.png]
[h4 Synopsis:]
template<class T>
template<class T>
std::complex<T> acos(const std::complex<T>& z);
__effects returns the inverse cosine of the complex number z.
__formula [$../images/acos.png]
@ -69,9 +69,9 @@ __formula [$../images/acos.png]
[h4 Synopsis:]
template<class T>
template<class T>
std::complex<T> atan(const std::complex<T>& z);
__effects returns the inverse tangent of the complex number z.
__formula [$../images/atan.png]
@ -86,9 +86,9 @@ __formula [$../images/atan.png]
[h4 Synopsis:]
template<class T>
template<class T>
std::complex<T> asinh(const std::complex<T>& z);
__effects returns the inverse hyperbolic sine of the complex number z.
__formula [$../images/asinh.png]
@ -103,9 +103,9 @@ __formula [$../images/asinh.png]
[h4 Synopsis:]
template<class T>
template<class T>
std::complex<T> acosh(const std::complex<T>& z);
__effects returns the inverse hyperbolic cosine of the complex number z.
__formula [$../images/acosh.png]
@ -120,9 +120,9 @@ __formula [$../images/acosh.png]
[h4 Synopsis:]
template<class T>
template<class T>
std::complex<T> atanh(const std::complex<T>& z);
__effects returns the inverse hyperbolic tangent of the complex number z.
__formula [$../images/atanh.png]
@ -139,5 +139,11 @@ __formula [$../images/atanh.png]
[endmathpart]
[/
Copyright 2008, 2009 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

2
doc/concepts/concepts.qbk
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@ -124,7 +124,7 @@ will all work with that type, and that's about it. If you want to use the distr
functions then you will need to provide your own wrapper header that:
* Provides std::numeric_limits<__float128> support.
* Provides overloads of the standard library math function for type __float128 and which forward to the libquadmath equivalents.
* Provides overloads of the standard library math function for type `__float128`and which forward to the libquadmath equivalents.
Ultimately these facilities should be provided by GCC and libstdc++.

14
doc/distributions/c_sharp.qbk
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@ -1,18 +1,18 @@
[section:c_sharp Using the Distributions from Within C#]
The distributions in this library can be used from the C# programming language
when they are built using Microsofts Common Language Runtime option.
when they are built using Microsoft's Common Language Runtime (CLR) option.
An example of this kind of usage is given in the
[@../../distexplorer/html/index.html distribution_explorer] example:
see =boost-root/libs/math/dot_net_example=
for the source code: the application consists of a C++ dll that contains the
An example of this kind of usage is given in the
[@../distexplorer/html/index.html Distribution Explorer]
example. See =boost-root/libs/math/dot_net_example=
for the source code: the application consists of a C++ .dll that contains the
actual distributions, and a C# GUI that allows you to explore their properties.
[endsect] [/section:c_sharp]
[/
Copyright 2006 John Maddock and Paul A. Bristow.
[/
Copyright 2006, 2013 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).

92
doc/distributions/chi_squared_examples.qbk
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@ -9,7 +9,7 @@ For this situation the Chi Squared distribution can be used to calculate
confidence intervals for the standard deviation.
The full example code & sample output is in
[@../../example/chi_square_std_dev_test.cpp chi_square_std_deviation_test.cpp].
[@../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp].
We'll begin by defining the procedure that will calculate and print out the
confidence intervals:
@ -18,7 +18,7 @@ confidence intervals:
double Sd, // Sample Standard Deviation
unsigned N) // Sample size
{
We'll begin by printing out some general information:
cout <<
@ -43,7 +43,7 @@ For each value of alpha, the formula for the confidence interval is given by:
[equation chi_squ_tut1]
Where [equation chi_squ_tut2] is the upper critical value, and
Where [equation chi_squ_tut2] is the upper critical value, and
[equation chi_squ_tut3] is the lower critical value of the
Chi Squared distribution.
@ -74,7 +74,7 @@ from the complement of the probability:
cout << endl;
To see some example output we'll use the
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm
gear data] from the __handbook.
The data represents measurements of gear diameter from a manufacturing
process.
@ -112,7 +112,7 @@ for the common confidence levels 95%, for increasing numbers of observations.
The standard deviation used to compute these values is unity,
so the limits listed are *multipliers* for any particular standard deviation.
For example, given a standard deviation of 0.0062789 as in the example
For example, given a standard deviation of 0.0062789 as in the example
above; for 100 observations the multiplier is 0.8780
giving the lower confidence limit of 0.8780 * 0.006728 = 0.00551.
@ -150,7 +150,7 @@ ________________________________________
With just 2 observations the limits are from *0.445* up to to *31.9*,
so the standard deviation might be about *half*
the observed value up to *30 times* the observed value!
the observed value up to [*30 times] the observed value!
Estimating a standard deviation with just a handful of values leaves a very great uncertainty,
especially the upper limit.
@ -168,7 +168,7 @@ Only when we have 10000 or more repeated observations can we start to be reasona
For 10000 observations, the interval is 0.99 to 1.1 - finally a really convincing + or -1% confidence.
[endsect][/section:chi_sq_intervals Confidence Intervals on the Standard Deviation]
[endsect] [/section:chi_sq_intervals Confidence Intervals on the Standard Deviation]
[section:chi_sq_test Chi-Square Test for the Standard Deviation]
@ -177,7 +177,7 @@ differs from a specified value. Typically this occurs in process change
situations where we wish to compare the standard deviation of a new
process to an established one.
The code for this example is contained in
The code for this example is contained in
[@../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp], and
we'll begin by defining the procedure that will print out the test
statistics:
@ -188,7 +188,7 @@ statistics:
unsigned N, // Sample size
double alpha) // Significance level
{
The procedure begins by printing a summary of the input data:
using namespace std;
@ -204,10 +204,10 @@ The procedure begins by printing a summary of the input data:
cout << setw(55) << left << "Sample Standard Deviation" << "= " << Sd << "\n";
cout << setw(55) << left << "Expected True Standard Deviation" << "= " << D << "\n\n";
The test statistic (T) is simply the ratio of the sample and "true" standard
deviations squared, multiplied by the number of degrees of freedom (the
The test statistic (T) is simply the ratio of the sample and "true" standard
deviations squared, multiplied by the number of degrees of freedom (the
sample size less one):
double t_stat = (N - 1) * (Sd / D) * (Sd / D);
cout << setw(55) << left << "Test Statistic" << "= " << t_stat << "\n";
@ -230,9 +230,9 @@ The various hypothesis that can be tested are summarised in the following table:
[ Reject if [chi][super 2][sub (alpha; N-1)] >= T ]]
]
Where [chi][super 2][sub (alpha; N-1)] is the upper critical value of the
Where [chi][super 2][sub (alpha; N-1)] is the upper critical value of the
Chi Squared distribution, and [chi][super 2][sub (1-alpha; N-1)] is the
lower critical value.
lower critical value.
Recall that the lower critical value is the same
as the quantile, and the upper critical value is the same as the quantile
@ -280,12 +280,12 @@ statistic, and print out the result of each hypothesis and test:
cout << endl << endl;
To see some example output we'll use the
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm
gear data] from the __handbook.
The data represents measurements of gear diameter from a manufacturing
process. The program output is deliberately designed to mirror
the DATAPLOT output shown in the
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm
process. The program output is deliberately designed to mirror
the DATAPLOT output shown in the
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm
NIST Handbook Example].
[pre'''
@ -316,13 +316,13 @@ In this case we are testing whether the sample standard deviation is 0.1,
and the null-hypothesis is rejected, so we conclude that the standard
deviation ['is not] 0.1.
For an alternative example, consider the
[@http://www.itl.nist.gov/div898/handbook/prc/section2/prc23.htm
For an alternative example, consider the
[@http://www.itl.nist.gov/div898/handbook/prc/section2/prc23.htm
silicon wafer data] again from the __handbook.
In this scenario a supplier of 100 ohm.cm silicon wafers claims
that his fabrication process can produce wafers with sufficient
consistency so that the standard deviation of resistivity for
the lot does not exceed 10 ohm.cm. A sample of N = 10 wafers taken
In this scenario a supplier of 100 ohm.cm silicon wafers claims
that his fabrication process can produce wafers with sufficient
consistency so that the standard deviation of resistivity for
the lot does not exceed 10 ohm.cm. A sample of N = 10 wafers taken
from the lot has a standard deviation of 13.97 ohm.cm, and the question
we ask ourselves is "Is the suppliers claim correct?".
@ -352,11 +352,11 @@ Standard Deviation < 10.000 REJECTED
Standard Deviation > 10.000 ACCEPTED
]
In this case, our null-hypothesis is that the standard deviation of
In this case, our null-hypothesis is that the standard deviation of
the sample is less than 10: this hypothesis is rejected in the analysis
above, and so we reject the manufacturers claim.
[endsect][/section:chi_sq_test Chi-Square Test for the Standard Deviation]
[endsect] [/section:chi_sq_test Chi-Square Test for the Standard Deviation]
[section:chi_sq_size Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation]
@ -364,16 +364,16 @@ Suppose we conduct a Chi Squared test for standard deviation and the result
is borderline, a legitimate question to ask is "How large would the sample size
have to be in order to produce a definitive result?"
The class template [link math_toolkit.dist_ref.dists.chi_squared_dist
chi_squared_distribution] has a static method
The class template [link math_toolkit.dist_ref.dists.chi_squared_dist
chi_squared_distribution] has a static method
`find_degrees_of_freedom` that will calculate this value for
some acceptable risk of type I failure /alpha/, type II failure
some acceptable risk of type I failure /alpha/, type II failure
/beta/, and difference from the standard deviation /diff/. Please
note that the method used works on variance, and not standard deviation
as is usual for the Chi Squared Test.
The code for this example is located in [@../../example/chi_square_std_dev_test.cpp
chi_square_std_dev_test.cpp].
The code for this example is located in
[@../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp].
We begin by defining a procedure to print out the sample sizes required
for various risk levels:
@ -407,7 +407,7 @@ where it is greater than the true value by /diff/. Thanks to the
asymmetric nature of the Chi Squared distribution these two values will
not be the same, the difference in their calculation differs only in the
sign of /diff/ that's passed to `find_degrees_of_freedom`. Finally
in this example we'll simply things, and let risk level /beta/ be the
in this example we'll simply things, and let risk level /beta/ be the
same as /alpha/:
cout << "\n\n"
@ -441,19 +441,19 @@ same as /alpha/:
}
cout << endl;
For some example output, consider the
[@http://www.itl.nist.gov/div898/handbook/prc/section2/prc23.htm
For some example output, consider the
[@http://www.itl.nist.gov/div898/handbook/prc/section2/prc23.htm
silicon wafer data] from the __handbook.
In this scenario a supplier of 100 ohm.cm silicon wafers claims
that his fabrication process can produce wafers with sufficient
consistency so that the standard deviation of resistivity for
the lot does not exceed 10 ohm.cm. A sample of N = 10 wafers taken
In this scenario a supplier of 100 ohm.cm silicon wafers claims
that his fabrication process can produce wafers with sufficient
consistency so that the standard deviation of resistivity for
the lot does not exceed 10 ohm.cm. A sample of N = 10 wafers taken
from the lot has a standard deviation of 13.97 ohm.cm, and the question
we ask ourselves is "How large would our sample have to be to reliably
detect this difference?".
To use our procedure above, we have to convert the
standard deviations to variance (square them),
standard deviations to variance (square them),
after which the program output looks like this:
[pre'''
@ -481,18 +481,18 @@ _______________________________________________________________
99.999 20 330'''
]
In this case we are interested in a upper single sided test.
In this case we are interested in a upper single sided test.
So for example, if the maximum acceptable risk of falsely rejecting
the null-hypothesis is 0.05 (Type I error), and the maximum acceptable
risk of failing to reject the null-hypothesis is also 0.05
the null-hypothesis is 0.05 (Type I error), and the maximum acceptable
risk of failing to reject the null-hypothesis is also 0.05
(Type II error), we estimate that we would need a sample size of 51.
[endsect][/section:chi_sq_size Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation]
[endsect] [/section:chi_sq_size Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation]
[endsect][/section:cs_eg Chi Squared Distribution]
[endsect] [/section:cs_eg Chi Squared Distribution]
[/
Copyright 2006 John Maddock and Paul A. Bristow.
[/
Copyright 2006, 2013 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).

18
doc/distributions/dist_reference.qbk
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@ -36,21 +36,21 @@
[include uniform.qbk]
[include weibull.qbk]
[endsect][/section:dists Distributions]
[endsect] [/section:dists Distributions]
[include dist_algorithms.qbk]
[endsect][/section:dist_ref Statistical Distributions and Functions Reference]
[endsect] [/section:dist_ref Statistical Distributions and Functions Reference]
[section:future Extras/Future Directions]
[h4 Adding Additional Location and Scale Parameters]
[h4 Adding Additional Location and Scale Parameters]
In some modelling applications we require a distribution
with a specific location and scale:
often this equates to a specific mean and standard deviation, although for many
distributions the relationship between these properties and the location and
distributions the relationship between these properties and the location and
scale parameters are non-trivial. See
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm]
for more information.
@ -61,7 +61,7 @@ The obvious way to handle this is via an adapter template:
class scaled_distribution
{
scaled_distribution(
const Dist dist,
const Dist dist,
typename Dist::value_type location,
typename Dist::value_type scale = 0);
};
@ -81,20 +81,20 @@ that conforms to the conceptual requirements of a distribution:
template <class Distribution>
any_distribution(const Distribution& d);
};
// Get the cdf of the underlying distribution:
template <class RealType>
RealType cdf(const any_distribution<RealType>& d, RealType x);
// etc....
Such a class would facilitate the writing of non-template code that can
Such a class would facilitate the writing of non-template code that can
function with any distribution type.
The [@http://sourceforge.net/projects/distexplorer/ Statistical Distribution Explorer]
utility for Windows is a usage example.
It's not clear yet whether there is a compelling use case though.
Possibly tests for goodness of fit might
Possibly tests for goodness of fit might
provide such a use case: this needs more investigation.
[h4 Higher Level Hypothesis Tests]

4
doc/html/backgrounders.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;15.&#160;Backgrounders</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="index.html" title="Math Toolkit">
<link rel="up" href="index.html" title="Math Toolkit">
<link rel="prev" href="math_toolkit/perf_test_app.html" title="The Performance Test Application">
@ -27,7 +27,7 @@
<a name="backgrounders"></a>Chapter&#160;15.&#160;Backgrounders</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dl>
<dt><span class="section"><a href="math_toolkit/sf_implementation.html">Additional Implementation
Notes</a></span></dt>
<dt><span class="section"><a href="math_toolkit/relative_error.html">Relative Error</a></span></dt>

4
doc/html/constants.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;6.&#160;Mathematical Constants</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="index.html" title="Math Toolkit">
<link rel="up" href="index.html" title="Math Toolkit">
<link rel="prev" href="math_toolkit/tr1_ref.html" title="TR1 C Functions Quick Reference">
@ -27,7 +27,7 @@
<a name="constants"></a>Chapter&#160;6.&#160;Mathematical Constants</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dl>
<dt><span class="section"><a href="math_toolkit/constants_intro.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial.html">Tutorial</a></span></dt>
<dd><dl>

4
doc/html/dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;2.&#160;Statistical Distributions and Functions</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="index.html" title="Math Toolkit">
<link rel="up" href="index.html" title="Math Toolkit">
<link rel="prev" href="math_toolkit/contact.html" title="Contact Info and Support">
@ -27,7 +27,7 @@
<a name="dist"></a>Chapter&#160;2.&#160;Statistical Distributions and Functions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dl>
<dt><span class="section"><a href="math_toolkit/stat_tut.html">Statistical Distributions Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Distributions</a></span></dt>

4
doc/html/extern_c.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;5.&#160;TR1 and C99 external "C" Functions</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="index.html" title="Math Toolkit">
<link rel="up" href="index.html" title="Math Toolkit">
<link rel="prev" href="math_toolkit/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">
@ -27,7 +27,7 @@
<a name="extern_c"></a>Chapter&#160;5.&#160;TR1 and C99 external "C" Functions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dl>
<dt><span class="section"><a href="math_toolkit/main_tr1.html">C99 and TR1 C Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/c99.html">C99 C Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tr1_ref.html">TR1 C Functions Quick Reference</a></span></dt>

4
doc/html/gcd_lcm.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;10.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="index.html" title="Math Toolkit">
<link rel="up" href="index.html" title="Math Toolkit">
<link rel="prev" href="math_toolkit/oct_todo.html" title="To Do">
@ -27,7 +27,7 @@
<a name="gcd_lcm"></a>Chapter&#160;10.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dl>
<dt><span class="section"><a href="math_toolkit/introduction.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_function_object.html">GCD Function Object</a></span></dt>

533
doc/html/index.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Math Toolkit</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="index.html" title="Math Toolkit">
<link rel="next" href="overview.html" title="Chapter&#160;1.&#160;Overview">
</head>
@ -76,31 +76,558 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
</div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dl>
<dt><span class="chapter"><a href="overview.html">1. Overview</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/main_intro.html">About the Math Toolkit</a></span></dt>
<dt><span class="section"><a href="math_toolkit/navigation.html">Navigation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/conventions.html">Document Conventions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/hints.html">Other Hints and tips</a></span></dt>
<dt><span class="section"><a href="math_toolkit/directories.html">Directory and File Structure</a></span></dt>
<dt><span class="section"><a href="math_toolkit/namespaces.html">Namespaces</a></span></dt>
<dt><span class="section"><a href="math_toolkit/result_type.html">Calculation of the Type of the
Result</a></span></dt>
<dt><span class="section"><a href="math_toolkit/error_handling.html">Error Handling</a></span></dt>
<dt><span class="section"><a href="math_toolkit/compilers_overview.html">Compilers</a></span></dt>
<dt><span class="section"><a href="math_toolkit/config_macros.html">Configuration Macros</a></span></dt>
<dt><span class="section"><a href="math_toolkit/intro_pol_overview.html">Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/threads.html">Thread Safety</a></span></dt>
<dt><span class="section"><a href="math_toolkit/perf_over1.html">Performance</a></span></dt>
<dt><span class="section"><a href="math_toolkit/building.html">If and How to Build a Boost.Math
Library, and its Examples and Tests</a></span></dt>
<dt><span class="section"><a href="math_toolkit/history1.html">History and What's New</a></span></dt>
<dt><span class="section"><a href="math_toolkit/overview_tr1.html">C99 and C++ TR1 C-style Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_faq.html">Frequently Asked Questions FAQ</a></span></dt>
<dt><span class="section"><a href="math_toolkit/contact.html">Contact Info and Support</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="dist.html">2. Statistical Distributions and Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut.html">Statistical Distributions Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/headers.html">Headers and
Namespaces</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/objects.html">Distributions
are Objects</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations
common to all distributions are non-member functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/complements.html">Complements
are supported too - and when to use them</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters
can be calculated</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution
Construction Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial
Distribution Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse
Chi-Squared Distribution Bayes Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi
Squared Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling
Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and
Scale Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with
C, R, FORTRAN-style Free Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions
from Within C#</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution
Parameters</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability
Distributions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and
Erlang) Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
Chi Squared Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse
Gamma Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse
Gaussian (or Inverse Normal) Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative
Binomial Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral
Beta Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
Chi-Squared Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian)
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew
Normal Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students
t Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/future.html">Extras/Future Directions</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="special.html">3. Special Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_gamma.html">Gamma Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_gamma/tgamma.html">Gamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/lgamma.html">Log Gamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/digamma.html">Digamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_ratios.html">Ratios of Gamma Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/igamma.html">Incomplete Gamma Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/igamma_inv.html">Incomplete Gamma Function
Inverses</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_derivatives.html">Derivative of
the Incomplete Gamma Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/factorials.html">Factorials and Binomial Coefficients</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/factorials/sf_factorial.html">Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_double_factorial.html">Double Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_rising_factorial.html">Rising Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_falling_factorial.html">Falling
Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_binomial.html">Binomial Coefficients</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sf_beta.html">Beta Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_beta/beta_function.html">Beta</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_beta/ibeta_function.html">Incomplete Beta
Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_beta/ibeta_inv_function.html">The Incomplete
Beta Function Inverses</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_beta/beta_derivative.html">Derivative of the
Incomplete Beta Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sf_erf.html">Error Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_erf/error_function.html">Error Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_erf/error_inv.html">Error Function Inverses</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sf_poly.html">Polynomials</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_poly/legendre.html">Legendre (and Associated)
Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_poly/laguerre.html">Laguerre (and Associated)
Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_poly/hermite.html">Hermite Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_poly/sph_harm.html">Spherical Harmonics</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/bessel.html">Bessel Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/bessel/bessel_over.html">Bessel Function Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/bessel_first.html">Bessel Functions of
the First and Second Kinds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/bessel_root.html">Finding Zeros of Bessel
Functions of the First and Second Kinds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/mbessel.html">Modified Bessel Functions
of the First and Second Kinds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/sph_bessel.html">Spherical Bessel Functions
of the First and Second Kinds</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/hankel.html">Hankel Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/hankel/cyl_hankel.html">Cyclic Hankel Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/hankel/sph_hankel.html">Spherical Hankel Functions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/airy.html">Airy Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/airy/ai.html">Airy Ai Function</a></span></dt>
<dt><span class="section"><a href="math_toolkit/airy/bi.html">Airy Bi Function</a></span></dt>
<dt><span class="section"><a href="math_toolkit/airy/aip.html">Airy Ai' Function</a></span></dt>
<dt><span class="section"><a href="math_toolkit/airy/bip.html">Airy Bi' Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/ellint.html">Elliptic Integrals</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_intro.html">Elliptic Integral Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_carlson.html">Elliptic Integrals
- Carlson Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_1.html">Elliptic Integrals of the
First Kind - Legendre Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_2.html">Elliptic Integrals of the
Second Kind - Legendre Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_3.html">Elliptic Integrals of the
Third Kind - Legendre Form</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/jacobi.html">Jacobi Elliptic Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/jacobi/jac_over.html">Overvew of the Jacobi Elliptic
Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_elliptic.html">Jacobi Elliptic
SN, CN and DN</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cd.html">Jacobi Elliptic Function
cd</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cn.html">Jacobi Elliptic Function
cn</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cs.html">Jacobi Elliptic Function
cs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dc.html">Jacobi Elliptic Function
dc</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dn.html">Jacobi Elliptic Function
dn</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ds.html">Jacobi Elliptic Function
ds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nc.html">Jacobi Elliptic Function
nc</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nd.html">Jacobi Elliptic Function
nd</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ns.html">Jacobi Elliptic Function
ns</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sc.html">Jacobi Elliptic Function
sc</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sd.html">Jacobi Elliptic Function
sd</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sn.html">Jacobi Elliptic Function
sn</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/zetas.html">Zeta Functions</a></span></dt>
<dd><dl><dt><span class="section"><a href="math_toolkit/zetas/zeta.html">Riemann Zeta Function</a></span></dt></dl></dd>
<dt><span class="section"><a href="math_toolkit/expint.html">Exponential Integrals</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/expint/expint_n.html">Exponential Integral En</a></span></dt>
<dt><span class="section"><a href="math_toolkit/expint/expint_i.html">Exponential Integral Ei</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/powers.html">Basic Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/powers/sin_pi.html">sin_pi</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/cos_pi.html">cos_pi</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/log1p.html">log1p</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/expm1.html">expm1</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/cbrt.html">cbrt</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/sqrt1pm1.html">sqrt1pm1</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/powm1.html">powm1</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/hypot.html">hypot</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/ct_pow.html">Compile Time Power of a Runtime
Base</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sinc.html">Sinus Cardinal and Hyperbolic Sinus
Cardinal Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sinc/sinc_overview.html">Sinus Cardinal and Hyperbolic
Sinus Cardinal Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sinc/sinc_pi.html">sinc_pi</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sinc/sinhc_pi.html">sinhc_pi</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/inv_hyper.html">Inverse Hyperbolic Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/inv_hyper/inv_hyper_over.html">Inverse Hyperbolic
Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/inv_hyper/acosh.html">acosh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/inv_hyper/asinh.html">asinh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/inv_hyper/atanh.html">atanh</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/owens_t.html">Owen's T function</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="utils.html">4. Floating Point Utilities</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/rounding.html">Rounding Truncation and Integer
Conversion</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/rounding/round.html">Rounding Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/rounding/trunc.html">Truncation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/rounding/modf.html">Integer and Fractional Part
Splitting (modf)</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/fpclass.html">Floating-Point Classification: Infinities
and NaNs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sign_functions.html">Sign Manipulation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets.html">Facets for Floating-Point Infinities
and NaNs</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/fp_facets/facets_intro.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/reference.html">Reference</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/examples.html">Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/portability.html">Portability</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/rationale.html">Design Rationale</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/next_float.html">Floating-Point Representation
Distance (ULP), and Finding Adjacent Floating-Point Values</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/next_float/nextafter.html">Finding the Next Representable
Value in a Specific Direction (nextafter)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_next.html">Finding the Next
Greater Representable Value (float_next)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_prior.html">Finding the Next
Smaller Representable Value (float_prior)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_distance.html">Calculating the
Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_advance.html">Advancing a Floating
Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
</dl></dd>
</dl></dd>
<dt><span class="chapter"><a href="extern_c.html">5. TR1 and C99 external "C" Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/main_tr1.html">C99 and TR1 C Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/c99.html">C99 C Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tr1_ref.html">TR1 C Functions Quick Reference</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="constants.html">6. Mathematical Constants</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/constants_intro.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial.html">Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/tutorial/non_templ.html">Use in non-template
code</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial/templ.html">Use in template code</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial/user_def.html">Use With User-Defined
Types</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/constants.html">The Mathematical Constants</a></span></dt>
<dt><span class="section"><a href="math_toolkit/new_const.html">Defining New Constants</a></span></dt>
<dt><span class="section"><a href="math_toolkit/constants_faq.html">FAQs</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="inverse_complex.html">7. Complex Number Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/complex_implementation.html">Implementation and
Accuracy</a></span></dt>
<dt><span class="section"><a href="math_toolkit/asin.html">asin</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acos.html">acos</a></span></dt>
<dt><span class="section"><a href="math_toolkit/atan.html">atan</a></span></dt>
<dt><span class="section"><a href="math_toolkit/asinh.html">asinh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acosh.html">acosh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/atanh.html">atanh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/complex_history.html">History</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="quaternions.html">8. Quaternions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/quat_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_header.html">Header File</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat.html">Template Class quaternion</a></span></dt>
<dt><span class="section"><a href="math_toolkit/spec.html">Quaternion Specializations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/mem_typedef.html">Quaternion Member Typedefs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_mem_fun.html">Quaternion Member Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_non_mem.html">Quaternion Non-Member Operators</a></span></dt>
<dt><span class="section"><a href="math_toolkit/value_op.html">Quaternion Value Operations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/create.html">Quaternion Creation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/trans.html">Quaternion Transcendentals</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_tests.html">Test Program</a></span></dt>
<dt><span class="section"><a href="math_toolkit/exp.html">The Quaternionic Exponential</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acknowledgement.html">Acknowledgements</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_history.html">History</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_todo.html">To Do</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="octonions.html">9. Octonions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/oct_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_header.html">Header File</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/octonion.html">Template Class octonion</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_specialization.html">Octonion Specializations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_typedefs.html">Octonion Member Typedefs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_mem_fun.html">Octonion Member Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_non_mem.html">Octonion Non-Member Operators</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_value_ops.html">Octonion Value Operations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_create.html">Octonion Creation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_trans.html">Octonions Transcendentals</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_tests.html">Test Program</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acknowledgements.html">Acknowledgements</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_history.html">History</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_todo.html">To Do</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="gcd_lcm.html">10. Integer Utilities (Greatest Common Divisor and Least Common Multiple)</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/introduction.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_function_object.html">GCD Function Object</a></span></dt>
<dt><span class="section"><a href="math_toolkit/lcm_function_object.html">LCM Function Object</a></span></dt>
<dt><span class="section"><a href="math_toolkit/run_time.html">Run-time GCD &amp; LCM Determination</a></span></dt>
<dt><span class="section"><a href="math_toolkit/compile_time.html">Compile time GCD and LCM determination</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_header.html">Header &lt;boost/math/common_factor.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="math_toolkit/demo.html">Demonstration Program</a></span></dt>
<dt><span class="section"><a href="math_toolkit/rationale.html">Rationale</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_history.html">History</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_credits.html">Credits</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="toolkit.html">11. Internals (Series, Rationals and Continued Fractions, Root Finding, Function
Minimization, Testing and Development Tools)</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/internals_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1.html">Utilities &amp; internals</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/internals1/series_evaluation.html">Series Evaluation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/cf.html">Continued Fraction Evaluation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/rational.html">Polynomial and Rational
Function Evaluation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/roots.html">Root Finding With Derivatives:
Newton-Raphson, Halley &amp; Schroeder</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/roots2.html">Root Finding Without
Derivatives: Bisection, Bracket and TOMS748</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/minima.html">Locating Function Minima:
Brent's algorithm</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/tuples.html">Tuples</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/internals2.html">Testing and Development</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/internals2/polynomials.html">Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals2/minimax.html">Minimax Approximations
and the Remez Algorithm</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals2/error_test.html">Relative Error and
Testing</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals2/test_data.html">Graphing, Profiling,
and Generating Test Data for Special Functions</a></span></dt>
</dl></dd>
</dl></dd>
<dt><span class="chapter"><a href="using_udt.html">12. Use with User-Defined Floating-Point Types - Boost.Multiprecision and
others</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/high_precision.html">Using Boost.Math with High-Precision
Floating-Point Libraries</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/high_precision/why_high_precision.html">Why use
a high-precision library rather than built-in floating-point types?</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/use_multiprecision.html">Using
Boost.Multiprecision</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/float128.html">Using with GCC's
__float128 datatype</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/use_mpfr.html">Using With MPFR
or GMP - High-Precision Floating-Point Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/e_float.html">Using e_float Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/use_ntl.html">Using NTL Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/using_test.html">Using without
expression templates for Boost.Test and others</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/concepts.html">Conceptual Requirements for Real
Number Types</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_concept.html">Conceptual Requirements for
Distribution Types</a></span></dt>
<dt><span class="section"><a href="math_toolkit/archetypes.html">Conceptual Archetypes for Reals
and Distributions</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="policy.html">13. Policies: Controlling Precision, Error Handling etc</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/pol_overview.html">Policy Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial.html">Policy Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/what_is_a_policy.html">So Just What
is a Policy Anyway?</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/policy_tut_defaults.html">Policies
Have Sensible Defaults</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/policy_usage.html">So How are Policies
Used Anyway?</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/changing_policy_defaults.html">Changing
the Policy Defaults</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/ad_hoc_dist_policies.html">Setting
Policies for Distributions on an Ad Hoc Basis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/ad_hoc_sf_policies.html">Changing
the Policy on an Ad Hoc Basis for the Special Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/namespace_policies.html">Setting
Policies at Namespace or Translation Unit Scope</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/user_def_err_pol.html">Calling User
Defined Error Handlers</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/understand_dis_quant.html">Understanding
Quantiles of Discrete Distributions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/pol_ref.html">Policy Reference</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/pol_ref/error_handling_policies.html">Error Handling
Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/internal_promotion.html">Internal Floating-point
Promotion Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/assert_undefined.html">Mathematically
Undefined Function Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/discrete_quant_ref.html">Discrete Quantile
Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/precision_pol.html">Precision Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/iteration_pol.html">Iteration Limits
Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/policy_defaults.html">Using Macros to
Change the Policy Defaults</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/namespace_pol.html">Setting Polices at
Namespace Scope</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/pol_ref_ref.html">Policy Class Reference</a></span></dt>
</dl></dd>
</dl></dd>
<dt><span class="chapter"><a href="perf.html">14. Performance</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/perf_over2.html">Performance Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/interp.html">Interpreting these Results</a></span></dt>
<dt><span class="section"><a href="math_toolkit/getting_best.html">Getting the Best Performance
from this Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/comp_compilers.html">Comparing Compilers</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tuning.html">Performance Tuning Macros</a></span></dt>
<dt><span class="section"><a href="math_toolkit/comparisons.html">Comparisons to Other Open Source
Libraries</a></span></dt>
<dt><span class="section"><a href="math_toolkit/perf_test_app.html">The Performance Test Application</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="backgrounders.html">15. Backgrounders</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_implementation.html">Additional Implementation
Notes</a></span></dt>
<dt><span class="section"><a href="math_toolkit/relative_error.html">Relative Error</a></span></dt>
<dt><span class="section"><a href="math_toolkit/lanczos.html">The Lanczos Approximation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/remez.html">The Remez Method</a></span></dt>
<dt><span class="section"><a href="math_toolkit/refs.html">References</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="status.html">16. Library Status</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/history2.html">History and What's New</a></span></dt>
<dt><span class="section"><a href="math_toolkit/issues.html">Known Issues, and TODO List</a></span></dt>
<dt><span class="section"><a href="math_toolkit/credits.html">Credits and Acknowledgements</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="indexes.html">17. Indexes</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="indexes/s01.html">Function Index</a></span></dt>
<dt><span class="section"><a href="indexes/s02.html">Class Index</a></span></dt>
<dt><span class="section"><a href="indexes/s03.html">Typedef Index</a></span></dt>
<dt><span class="section"><a href="indexes/s04.html">Macro Index</a></span></dt>
<dt><span class="section"><a href="indexes/s05.html">Index</a></span></dt>
</dl></dd>
</dl>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: May 16, 2013 at 08:52:38 GMT</small></p></td>
<td align="left"><p><small>Last revised: May 17, 2013 at 11:02:56 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
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<dt><span class="section"><a href="indexes/s01.html">Function Index</a></span></dt>
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<a name="id1519274"></a>Function Index</h2></div></div></div>
<p><a class="link" href="s01.html#idx_id_0">A</a> <a class="link" href="s01.html#idx_id_1">B</a> <a class="link" href="s01.html#idx_id_2">C</a> <a class="link" href="s01.html#idx_id_3">D</a> <a class="link" href="s01.html#idx_id_4">E</a> <a class="link" href="s01.html#idx_id_5">F</a> <a class="link" href="s01.html#idx_id_6">G</a> <a class="link" href="s01.html#idx_id_7">H</a> <a class="link" href="s01.html#idx_id_8">I</a> <a class="link" href="s01.html#idx_id_9">J</a> <a class="link" href="s01.html#idx_id_10">K</a> <a class="link" href="s01.html#idx_id_11">L</a> <a class="link" href="s01.html#idx_id_12">M</a> <a class="link" href="s01.html#idx_id_13">N</a> <a class="link" href="s01.html#idx_id_14">O</a> <a class="link" href="s01.html#idx_id_15">P</a> <a class="link" href="s01.html#idx_id_16">Q</a> <a class="link" href="s01.html#idx_id_17">R</a> <a class="link" href="s01.html#idx_id_18">S</a> <a class="link" href="s01.html#idx_id_19">T</a> <a class="link" href="s01.html#idx_id_20">U</a> <a class="link" href="s01.html#idx_id_21">V</a> <a class="link" href="s01.html#idx_id_22">W</a> <a class="link" href="s01.html#idx_id_23">Z</a></p>
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<dt>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies"><span class="index-entry-level-1">Discrete Quantile Policies</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/future.html" title="Extras/Future Directions"><span class="index-entry-level-1">Extras/Future Directions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/generic.html" title="Generic operations common to all distributions are non-member functions"><span class="index-entry-level-1">Generic operations common to all distributions are non-member functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">Negative Binomial Sales Quota Example.</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/nmp.html" title="Non-Member Properties"><span class="index-entry-level-1">Non-Member Properties</span></a></p></li>
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<p><a class="link" href="s04.html#idx_id_73">B</a> <a class="link" href="s04.html#idx_id_77">F</a></p>
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@ -1107,6 +1107,7 @@
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies"><span class="index-entry-level-1">Discrete Quantile Policies</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/future.html" title="Extras/Future Directions"><span class="index-entry-level-1">Extras/Future Directions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/generic.html" title="Generic operations common to all distributions are non-member functions"><span class="index-entry-level-1">Generic operations common to all distributions are non-member functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">Negative Binomial Sales Quota Example.</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/nmp.html" title="Non-Member Properties"><span class="index-entry-level-1">Non-Member Properties</span></a></p></li>
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@ -3699,6 +3700,7 @@
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">BOOST_MATH_OVERFLOW_ERROR_POLICY</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">cdf</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">expression</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">quantile</span></a></p></li>
</ul></div>

4
doc/html/inverse_complex.html
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@ -27,7 +27,7 @@
<a name="inverse_complex"></a>Chapter&#160;7.&#160;Complex Number Functions</h1></div></div></div>
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<p><b>Table of Contents</b></p>
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<dl>
<dt><span class="section"><a href="math_toolkit/complex_implementation.html">Implementation and
Accuracy</a></span></dt>
<dt><span class="section"><a href="math_toolkit/asin.html">asin</a></span></dt>

4
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<a name="math_toolkit.acknowledgement"></a><a class="link" href="acknowledgement.html" title="Acknowledgements">Acknowledgements</a>
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4
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4
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4
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6
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<dt><span class="section"><a href="airy/bi.html">Airy Bi Function</a></span></dt>
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4
doc/html/math_toolkit/airy/ai.html
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4
doc/html/math_toolkit/airy/aip.html
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4
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4
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4
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4
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4
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4
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28
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@ -344,7 +344,7 @@
</td>
<td>
<p>
+INF <a href="#ftn.math_toolkit.comparisons.f0" class="footnote" name="math_toolkit.comparisons.f0"><sup class="footnote">[1]</sup></a>
+INF <a href="#ftn.math_toolkit.comparisons.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f0"></a>[1]</sup></a>
</p>
</td>
</tr>
@ -423,7 +423,7 @@
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<p>
</p>
<p>17.89<a href="#ftn.math_toolkit.comparisons.f1" class="footnote" name="math_toolkit.comparisons.f1"><sup class="footnote">[2]</sup></a></p>
<p>17.89<a href="#ftn.math_toolkit.comparisons.f1" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f1"></a>[2]</sup></a></p>
<p> </p>
<p>(4.248e-005s)</p>
<p>
@ -659,7 +659,7 @@
<td>
<p>
</p>
<p>67.66<a href="#ftn.math_toolkit.comparisons.f2" class="footnote" name="math_toolkit.comparisons.f2"><sup class="footnote">[1]</sup></a></p>
<p>67.66<a href="#ftn.math_toolkit.comparisons.f2" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f2"></a>[1]</sup></a></p>
<p> </p>
<p>(3.366e-004s)</p>
<p>
@ -1089,7 +1089,7 @@
<td>
<p>
</p>
<p>3.60<a href="#ftn.math_toolkit.comparisons.f3" class="footnote" name="math_toolkit.comparisons.f3"><sup class="footnote">[2]</sup></a></p>
<p>3.60<a href="#ftn.math_toolkit.comparisons.f3" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f3"></a>[2]</sup></a></p>
<p> </p>
<p>(5.987e-007s)</p>
<p>
@ -1319,7 +1319,7 @@
<td>
<p>
</p>
<p>43.43<a href="#ftn.math_toolkit.comparisons.f4" class="footnote" name="math_toolkit.comparisons.f4"><sup class="footnote">[3]</sup></a></p>
<p>43.43<a href="#ftn.math_toolkit.comparisons.f4" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f4"></a>[3]</sup></a></p>
<p> </p>
<p>(3.732e-004s)</p>
<p>
@ -1389,7 +1389,7 @@
<td>
<p>
</p>
<p>393.90<a href="#ftn.math_toolkit.comparisons.f5" class="footnote" name="math_toolkit.comparisons.f5"><sup class="footnote">[4]</sup></a></p>
<p>393.90<a href="#ftn.math_toolkit.comparisons.f5" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f5"></a>[4]</sup></a></p>
<p> </p>
<p>(2.673e-002s)</p>
<p>
@ -1525,7 +1525,7 @@
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f6" class="footnote" name="math_toolkit.comparisons.f6"><sup class="footnote">[5]</sup></a></p>
<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f6" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f6"></a>[5]</sup></a></p>
<p> </p>
<p>(4.411e-004s)</p>
<p>
@ -1936,7 +1936,7 @@
<td>
<p>
</p>
<p>30.51<a href="#ftn.math_toolkit.comparisons.f7" class="footnote" name="math_toolkit.comparisons.f7"><sup class="footnote">[1]</sup></a></p>
<p>30.51<a href="#ftn.math_toolkit.comparisons.f7" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f7"></a>[1]</sup></a></p>
<p> </p>
<p>(3.616e-004s)</p>
<p>
@ -2366,7 +2366,7 @@
<td>
<p>
</p>
<p>2.20<a href="#ftn.math_toolkit.comparisons.f8" class="footnote" name="math_toolkit.comparisons.f8"><sup class="footnote">[2]</sup></a></p>
<p>2.20<a href="#ftn.math_toolkit.comparisons.f8" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f8"></a>[2]</sup></a></p>
<p> </p>
<p>(3.522e-007s)</p>
<p>
@ -2596,7 +2596,7 @@
<td>
<p>
</p>
<p>25.92<a href="#ftn.math_toolkit.comparisons.f9" class="footnote" name="math_toolkit.comparisons.f9"><sup class="footnote">[3]</sup></a></p>
<p>25.92<a href="#ftn.math_toolkit.comparisons.f9" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f9"></a>[3]</sup></a></p>
<p> </p>
<p>(4.407e-004s)</p>
<p>
@ -2666,7 +2666,7 @@
<td>
<p>
</p>
<p>144.91<a href="#ftn.math_toolkit.comparisons.f10" class="footnote" name="math_toolkit.comparisons.f10"><sup class="footnote">[4]</sup></a></p>
<p>144.91<a href="#ftn.math_toolkit.comparisons.f10" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f10"></a>[4]</sup></a></p>
<p> </p>
<p>(3.214e-002s)</p>
<p>
@ -2802,7 +2802,7 @@
<td>
<p>
</p>
<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f11" class="footnote" name="math_toolkit.comparisons.f11"><sup class="footnote">[5]</sup></a></p>
<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f11" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f11"></a>[5]</sup></a></p>
<p> </p>
<p>(5.916e-004s)</p>
<p>

4
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@ -3,7 +3,7 @@
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4
doc/html/math_toolkit/complex_history.html
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@ -3,7 +3,7 @@
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4
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4
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4
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<p>
<a class="indexterm" name="id856043"></a>
<a class="indexterm" name="id939682"></a>
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<p>
This documentation aims to use of the following naming and formatting conventions.

4
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4
doc/html/math_toolkit/directories.html
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4
doc/html/math_toolkit/dist_concept.html
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.dist_concept"></a><a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for
Distribution Types</a>

6
doc/html/math_toolkit/dist_ref.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
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<div class="section math_toolkit_dist_ref">
<div class="section math_toolkit_dist_ref">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.dist_ref"></a><a class="link" href="dist_ref.html" title="Statistical Distributions Reference">Statistical Distributions Reference</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<div class="toc"><dl>
<dt><span class="section"><a href="dist_ref/nmp.html">Non-Member Properties</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists.html">Distributions</a></span></dt>
<dd><dl>

4
doc/html/math_toolkit/dist_ref/dist_algorithms.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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@ -22,7 +22,7 @@
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<div class="section math_toolkit_dist_ref_dist_algorithms">
<div class="section math_toolkit_dist_ref_dist_algorithms">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a>
</h3></div></div></div>

6
doc/html/math_toolkit/dist_ref/dists.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distributions</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
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@ -22,11 +22,11 @@
<div class="spirit-nav">
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</div>
<div class="section math_toolkit_dist_ref_dists">
<div class="section math_toolkit_dist_ref_dists">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist_ref.dists"></a><a class="link" href="dists.html" title="Distributions">Distributions</a>
</h3></div></div></div>
<div class="toc"><dl class="toc">
<div class="toc"><dl>
<dt><span class="section"><a href="dists/bernoulli_dist.html">Bernoulli
Distribution</a></span></dt>
<dt><span class="section"><a href="dists/beta_dist.html">Beta Distribution</a></span></dt>

4
doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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@ -22,7 +22,7 @@
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</div>
<div class="section math_toolkit_dist_ref_dists_bernoulli_dist">
<div class="section math_toolkit_dist_ref_dists_bernoulli_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.bernoulli_dist"></a><a class="link" href="bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/beta_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Beta Distribution</title>
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@ -22,7 +22,7 @@
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</div>
<div class="section math_toolkit_dist_ref_dists_beta_dist">
<div class="section math_toolkit_dist_ref_dists_beta_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.beta_dist"></a><a class="link" href="beta_dist.html" title="Beta Distribution">Beta Distribution</a>
</h4></div></div></div>

4
doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Binomial Distribution</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
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@ -22,7 +22,7 @@
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</div>
<div class="section math_toolkit_dist_ref_dists_binomial_dist">
<div class="section math_toolkit_dist_ref_dists_binomial_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.binomial_dist"></a><a class="link" href="binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Cauchy-Lorentz Distribution</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
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@ -22,7 +22,7 @@
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</div>
<div class="section math_toolkit_dist_ref_dists_cauchy_dist">
<div class="section math_toolkit_dist_ref_dists_cauchy_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.cauchy_dist"></a><a class="link" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chi Squared Distribution</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
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<link rel="prev" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
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</div>
<div class="section math_toolkit_dist_ref_dists_chi_squared_dist">
<div class="section math_toolkit_dist_ref_dists_chi_squared_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.chi_squared_dist"></a><a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/exp_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exponential Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="chi_squared_dist.html" title="Chi Squared Distribution">
@ -22,7 +22,7 @@
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</div>
<div class="section math_toolkit_dist_ref_dists_exp_dist">
<div class="section math_toolkit_dist_ref_dists_exp_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.exp_dist"></a><a class="link" href="exp_dist.html" title="Exponential Distribution">Exponential Distribution</a>
</h4></div></div></div>

4
doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Extreme Value Distribution</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="exp_dist.html" title="Exponential Distribution">
@ -22,7 +22,7 @@
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</div>
<div class="section math_toolkit_dist_ref_dists_extreme_dist">
<div class="section math_toolkit_dist_ref_dists_extreme_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.extreme_dist"></a><a class="link" href="extreme_dist.html" title="Extreme Value Distribution">Extreme Value
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/f_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>F Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="extreme_dist.html" title="Extreme Value Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
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</div>
<div class="section math_toolkit_dist_ref_dists_f_dist">
<div class="section math_toolkit_dist_ref_dists_f_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.f_dist"></a><a class="link" href="f_dist.html" title="F Distribution">F Distribution</a>
</h4></div></div></div>

4
doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Gamma (and Erlang) Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
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<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="f_dist.html" title="F Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="geometric_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_gamma_dist">
<div class="section math_toolkit_dist_ref_dists_gamma_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.gamma_dist"></a><a class="link" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and
Erlang) Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Geometric Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_geometric_dist">
<div class="section math_toolkit_dist_ref_dists_geometric_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.geometric_dist"></a><a class="link" href="geometric_dist.html" title="Geometric Distribution">Geometric
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Hypergeometric Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="geometric_dist.html" title="Geometric Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="geometric_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_chi_squared_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_hypergeometric_dist">
<div class="section math_toolkit_dist_ref_dists_hypergeometric_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.hypergeometric_dist"></a><a class="link" href="hypergeometric_dist.html" title="Hypergeometric Distribution">Hypergeometric
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Chi Squared Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="hypergeometric_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_gamma_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_inverse_chi_squared_dist">
<div class="section math_toolkit_dist_ref_dists_inverse_chi_squared_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.inverse_chi_squared_dist"></a><a class="link" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
Chi Squared Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Gamma Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="inverse_chi_squared_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_gaussian_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_inverse_gamma_dist">
<div class="section math_toolkit_dist_ref_dists_inverse_gamma_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.inverse_gamma_dist"></a><a class="link" href="inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
Gamma Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Gaussian (or Inverse Normal) Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="inverse_gamma_dist.html" title="Inverse Gamma Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="inverse_gamma_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="laplace_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_inverse_gaussian_dist">
<div class="section math_toolkit_dist_ref_dists_inverse_gaussian_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.inverse_gaussian_dist"></a><a class="link" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">Inverse
Gaussian (or Inverse Normal) Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/laplace_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Laplace Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="inverse_gaussian_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="logistic_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_laplace_dist">
<div class="section math_toolkit_dist_ref_dists_laplace_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.laplace_dist"></a><a class="link" href="laplace_dist.html" title="Laplace Distribution">Laplace Distribution</a>
</h4></div></div></div>

4
doc/html/math_toolkit/dist_ref/dists/logistic_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Logistic Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="laplace_dist.html" title="Laplace Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="laplace_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_logistic_dist">
<div class="section math_toolkit_dist_ref_dists_logistic_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.logistic_dist"></a><a class="link" href="logistic_dist.html" title="Logistic Distribution">Logistic
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Log Normal Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="logistic_dist.html" title="Logistic Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_lognormal_dist">
<div class="section math_toolkit_dist_ref_dists_lognormal_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.lognormal_dist"></a><a class="link" href="lognormal_dist.html" title="Log Normal Distribution">Log Normal
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral Beta Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="negative_binomial_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="nc_chi_squared_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_nc_beta_dist">
<div class="section math_toolkit_dist_ref_dists_nc_beta_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.nc_beta_dist"></a><a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral
Beta Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral Chi-Squared Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="nc_beta_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="nc_f_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_nc_chi_squared_dist">
<div class="section math_toolkit_dist_ref_dists_nc_chi_squared_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.nc_chi_squared_dist"></a><a class="link" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
Chi-Squared Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral F Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="nc_chi_squared_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="nc_t_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_nc_f_dist">
<div class="section math_toolkit_dist_ref_dists_nc_f_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.nc_f_dist"></a><a class="link" href="nc_f_dist.html" title="Noncentral F Distribution">Noncentral F
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral T Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_f_dist.html" title="Noncentral F Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="nc_f_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="normal_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_nc_t_dist">
<div class="section math_toolkit_dist_ref_dists_nc_t_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.nc_t_dist"></a><a class="link" href="nc_t_dist.html" title="Noncentral T Distribution">Noncentral T
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Negative Binomial Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="lognormal_dist.html" title="Log Normal Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="lognormal_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="nc_beta_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_negative_binomial_dist">
<div class="section math_toolkit_dist_ref_dists_negative_binomial_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.negative_binomial_dist"></a><a class="link" href="negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
Binomial Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/normal_dist.html
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@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Normal (Gaussian) Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_t_dist.html" title="Noncentral T Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="pareto.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_normal_dist">
<div class="section math_toolkit_dist_ref_dists_normal_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.normal_dist"></a><a class="link" href="normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian)
Distribution</a>

4
doc/html/math_toolkit/dist_ref/dists/pareto.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Pareto Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="normal_dist.html" title="Normal (Gaussian) Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="normal_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="poisson_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_pareto">
<div class="section math_toolkit_dist_ref_dists_pareto">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.pareto"></a><a class="link" href="pareto.html" title="Pareto Distribution">Pareto Distribution</a>
</h4></div></div></div>

4
doc/html/math_toolkit/dist_ref/dists/poisson_dist.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Poisson Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="pareto.html" title="Pareto Distribution">
@ -22,7 +22,7 @@
<div class="spirit-nav">
<a accesskey="p" href="pareto.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rayleigh.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section math_toolkit_dist_ref_dists_poisson_dist">
<div class="section math_toolkit_dist_ref_dists_poisson_dist">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist_ref.dists.poisson_dist"></a><a class="link" href="poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a>
</h4></div></div></div>

4
doc/html/math_toolkit/dist_ref/dists/rayleigh.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rayleigh Distribution</title>
<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
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<a name="math_toolkit.dist_ref.dists.rayleigh"></a><a class="link" href="rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a>
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4
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@ -3,7 +3,7 @@
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4
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@ -3,7 +3,7 @@
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@ -3,7 +3,7 @@
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4
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@ -3,7 +3,7 @@
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<div class="toc"><dl class="toc">
<div class="toc"><dl>
<dt><span class="section"><a href="ellint/ellint_intro.html">Elliptic Integral Overview</a></span></dt>
<dt><span class="section"><a href="ellint/ellint_carlson.html">Elliptic Integrals
- Carlson Form</a></span></dt>

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@ -3,7 +3,7 @@
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@ -3,7 +3,7 @@
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Third Kind - Legendre Form</a>
@ -274,7 +274,7 @@
<span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) + 2m&#928;(n, k) ; n &lt;= 1</em></span>
</p>
<p>
<span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) ; n &gt; 1</em></span> <a href="#ftn.math_toolkit.ellint.ellint_3.f0" class="footnote" name="math_toolkit.ellint.ellint_3.f0"><sup class="footnote">[1]</sup></a>
<span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) ; n &gt; 1</em></span> <a href="#ftn.math_toolkit.ellint.ellint_3.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.ellint.ellint_3.f0"></a>[1]</sup></a>
</p>
<p>
are used to move &#966; &#160; to the range [0, &#960;/2].
@ -293,7 +293,7 @@
<span class="inlinemediaobject"><img src="../../../equations/ellint26.png"></span>
</p>
<div class="footnotes">
<br><hr style="width:100; text-align:left;margin-left: 0">
<br><hr style="width:100; align:left;">
<div id="ftn.math_toolkit.ellint.ellint_3.f0" class="footnote"><p><a href="#math_toolkit.ellint.ellint_3.f0" class="para"><sup class="para">[1] </sup></a>
I haven't been able to find a literature reference for this relation, but
it appears to be the convention used by Mathematica. Intuitively the first

4
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