| <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 V1.77.1"> |
| <link rel="home" href="index.html" title="Math Toolkit 2.2.0"> |
| <link rel="up" href="index.html" title="Math Toolkit 2.2.0"> |
| <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 href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../more/index.htm">More</a></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> |
| <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> |
| <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> |
| <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/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/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> |
| <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<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>) |
| </p> |
| </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> |
