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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 5. Statistical Distributions and Functions</title> <link rel="stylesheet" href="math.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> <link rel="home" href="index.html" title="Math Toolkit 2.1.0"> <link rel="up" href="index.html" title="Math Toolkit 2.1.0"> <link rel="prev" href="math_toolkit/constants_faq.html" title="FAQs"> <link rel="next" href="math_toolkit/stat_tut.html" title="Statistical Distributions Tutorial"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td> <td align="center"><a href="../../../../index.html">Home</a></td> <td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a 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<dt><a href="math_toolkit/stat_tut/overview.html">Overview of Distributions</a></dt> <dd><dl> <dt><a href="math_toolkit/stat_tut/overview/headers.html">Headers and Namespaces</a></dt> <dt><a href="math_toolkit/stat_tut/overview/objects.html">Distributions are Objects</a></dt> <dt><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations common to all distributions are non-member functions</a></dt> <dt><a href="math_toolkit/stat_tut/overview/complements.html">Complements are supported too - and when to use them</a></dt> <dt><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters can be calculated</a></dt> <dt><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></dt> <dd><dl> <dt><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution Construction Examples</a></dt> <dt><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution Examples</a></dt> <dd><dl> <dt><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></dt> <dt><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html">Testing a sample mean for difference from a "true" mean</a></dt> <dt><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></dt> <dt><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></dt> <dt><a href="math_toolkit/stat_tut/weg/st_eg/paired_st.html">Comparing two paired samples with the Student's t distribution</a></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution Examples</a></dt> <dd><dl> <dt><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence Intervals on the Standard Deviation</a></dt> <dt><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square Test for the Standard Deviation</a></dt> <dt><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></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></dt> <dt><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution Examples</a></dt> <dd><dl> <dt><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial Coin-Flipping Example</a></dt> <dt><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial Quiz Example</a></dt> <dt><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></dt> <dt><a href="math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating Sample Sizes for a Binomial Distribution.</a></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution Examples</a></dt> <dt><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial Distribution Examples</a></dt> <dd><dl> <dt><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></dt> <dt><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating Sample Sizes for the Negative Binomial.</a></dt> <dt><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative Binomial Sales Quota Example.</a></dt> <dt><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative Binomial Table Printing Example.</a></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution Examples</a></dt> <dd><dl><dt><a href="math_toolkit/stat_tut/weg/normal_example/normal_misc.html">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd> <dt><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse Chi-Squared Distribution Bayes Example</a></dt> <dt><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi Squared Example</a></dt> <dd><dl><dt><a href="math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables of the power function of the chi2 test.</a></dt></dl></dd> <dt><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling Example</a></dt> <dt><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and Scale Examples</a></dt> <dd><dl> <dt><a href="math_toolkit/stat_tut/weg/find_eg/find_location_eg.html">Find Location (Mean) Example</a></dt> <dt><a href="math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html">Find Scale (Standard Deviation) Example</a></dt> <dt><a href="math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find mean and standard deviation example</a></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with C, R, FORTRAN-style Free Functions</a></dt> <dt><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions from Within C#</a></dt> </dl></dd> <dt><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution Parameters</a></dt> <dt><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability Distributions</a></dt> </dl></dd> <dt><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></dt> <dd><dl> <dt><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></dt> <dt><a href="math_toolkit/dist_ref/dists.html">Distributions</a></dt> <dd><dl> <dt><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and Erlang) Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/hyperexponential_dist.html">Hyperexponential Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse Chi Squared Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse Gamma Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse Gaussian (or Inverse Normal) Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative Binomial Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral Beta Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral Chi-Squared Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian) Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew Normal Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students t Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></dt> <dt><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></dt> </dl></dd> <dt><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></dt> </dl></dd> <dt><a href="math_toolkit/future.html">Extras/Future Directions</a></dt> </dl> </div> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang 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>) </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="math_toolkit/constants_faq.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="index.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="math_toolkit/stat_tut.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>