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<title>Chapter 5. Statistical Distributions and Functions</title>
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<div class="chapter">
<div class="titlepage"><div><div><h1 class="title">
<a name="dist"></a>Chapter 5. Statistical Distributions and Functions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<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 Statistical
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>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating
confidence intervals on the mean with the Students-t distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html">Testing
a sample mean for difference from a "true" mean</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html">Estimating
how large a sample size would have to become in order to give a significant
Students-t test result with a single sample test</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html">Comparing
the means of two samples with the Students-t test</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/paired_st.html">Comparing
two paired samples with the Student's t distribution</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution
Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence
Intervals on the Standard Deviation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square
Test for the Standard Deviation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html">Estimating
the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></span></dt>
</dl></dd>
<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>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial
Coin-Flipping Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial
Quiz Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_conf.html">Calculating
Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating
Sample Sizes for a Binomial Distribution.</a></span></dt>
</dl></dd>
<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>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating
Confidence Limits on the Frequency of Occurrence for the Negative Binomial
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
Sample Sizes for the Negative Binomial.</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative
Binomial Sales Quota Example.</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative
Binomial Table Printing Example.</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution
Examples</a></span></dt>
<dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example/normal_misc.html">Some
Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
<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>
<dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables
of the power function of the chi<sup>2</sup> test.</a></span></dt></dl></dd>
<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>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_location_eg.html">Find
Location (Mean) Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html">Find
Scale (Standard Deviation) Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find
mean and standard deviation example</a></span></dt>
</dl></dd>
<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/arcine_dist.html">Arcsine Distribution</a></span></dt>
<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/empirical_cdf.html">Empirical
Cumulative Distribution Function</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/hyperexponential_dist.html">Hyperexponential
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/kolmogorov_smirnov_dist.html">Kolmogorov-Smirnov
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>
</div>
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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