1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Chapter 5. Statistical Distributions and Functions</title> 5<link rel="stylesheet" href="math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="index.html" title="Math Toolkit 2.12.0"> 9<link rel="prev" href="math_toolkit/constants_faq.html" title="Math Constants FAQs"> 10<link rel="next" href="math_toolkit/stat_tut.html" title="Statistical Distributions Tutorial"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td> 15<td align="center"><a href="../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<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> 24</div> 25<div class="chapter"> 26<div class="titlepage"><div><div><h1 class="title"> 27<a name="dist"></a>Chapter 5. Statistical Distributions and Functions</h1></div></div></div> 28<div class="toc"> 29<p><b>Table of Contents</b></p> 30<dl class="toc"> 31<dt><span class="section"><a href="math_toolkit/stat_tut.html">Statistical Distributions Tutorial</a></span></dt> 32<dd><dl> 33<dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Statistical 34 Distributions</a></span></dt> 35<dd><dl> 36<dt><span class="section"><a href="math_toolkit/stat_tut/overview/headers.html">Headers and 37 Namespaces</a></span></dt> 38<dt><span class="section"><a href="math_toolkit/stat_tut/overview/objects.html">Distributions 39 are Objects</a></span></dt> 40<dt><span class="section"><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations 41 common to all distributions are non-member functions</a></span></dt> 42<dt><span class="section"><a href="math_toolkit/stat_tut/overview/complements.html">Complements 43 are supported too - and when to use them</a></span></dt> 44<dt><span class="section"><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters 45 can be calculated</a></span></dt> 46<dt><span class="section"><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></span></dt> 47</dl></dd> 48<dt><span class="section"><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></span></dt> 49<dd><dl> 50<dt><span class="section"><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution 51 Construction Examples</a></span></dt> 52<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution 53 Examples</a></span></dt> 54<dd><dl> 55<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating 56 confidence intervals on the mean with the Students-t distribution</a></span></dt> 57<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html">Testing 58 a sample mean for difference from a "true" mean</a></span></dt> 59<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html">Estimating 60 how large a sample size would have to become in order to give a significant 61 Students-t test result with a single sample test</a></span></dt> 62<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html">Comparing 63 the means of two samples with the Students-t test</a></span></dt> 64<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/paired_st.html">Comparing 65 two paired samples with the Student's t distribution</a></span></dt> 66</dl></dd> 67<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution 68 Examples</a></span></dt> 69<dd><dl> 70<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence 71 Intervals on the Standard Deviation</a></span></dt> 72<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square 73 Test for the Standard Deviation</a></span></dt> 74<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html">Estimating 75 the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></span></dt> 76</dl></dd> 77<dt><span class="section"><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></span></dt> 78<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution 79 Examples</a></span></dt> 80<dd><dl> 81<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial 82 Coin-Flipping Example</a></span></dt> 83<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial 84 Quiz Example</a></span></dt> 85<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_conf.html">Calculating 86 Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></span></dt> 87<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating 88 Sample Sizes for a Binomial Distribution.</a></span></dt> 89</dl></dd> 90<dt><span class="section"><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution 91 Examples</a></span></dt> 92<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial 93 Distribution Examples</a></span></dt> 94<dd><dl> 95<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating 96 Confidence Limits on the Frequency of Occurrence for the Negative Binomial 97 Distribution</a></span></dt> 98<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating 99 Sample Sizes for the Negative Binomial.</a></span></dt> 100<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative 101 Binomial Sales Quota Example.</a></span></dt> 102<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative 103 Binomial Table Printing Example.</a></span></dt> 104</dl></dd> 105<dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution 106 Examples</a></span></dt> 107<dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example/normal_misc.html">Some 108 Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd> 109<dt><span class="section"><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse 110 Chi-Squared Distribution Bayes Example</a></span></dt> 111<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi 112 Squared Example</a></span></dt> 113<dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables 114 of the power function of the chi<sup>2</sup> test.</a></span></dt></dl></dd> 115<dt><span class="section"><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling 116 Example</a></span></dt> 117<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and 118 Scale Examples</a></span></dt> 119<dd><dl> 120<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_location_eg.html">Find 121 Location (Mean) Example</a></span></dt> 122<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html">Find 123 Scale (Standard Deviation) Example</a></span></dt> 124<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find 125 mean and standard deviation example</a></span></dt> 126</dl></dd> 127<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with 128 C, R, FORTRAN-style Free Functions</a></span></dt> 129<dt><span class="section"><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions 130 from Within C#</a></span></dt> 131</dl></dd> 132<dt><span class="section"><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution 133 Parameters</a></span></dt> 134<dt><span class="section"><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability 135 Distributions</a></span></dt> 136</dl></dd> 137<dt><span class="section"><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></span></dt> 138<dd><dl> 139<dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt> 140<dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt> 141<dd><dl> 142<dt><span class="section"><a href="math_toolkit/dist_ref/dists/arcine_dist.html">Arcsine Distribution</a></span></dt> 143<dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli 144 Distribution</a></span></dt> 145<dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt> 146<dt><span class="section"><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial 147 Distribution</a></span></dt> 148<dt><span class="section"><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz 149 Distribution</a></span></dt> 150<dt><span class="section"><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared 151 Distribution</a></span></dt> 152<dt><span class="section"><a href="math_toolkit/dist_ref/dists/empirical_cdf.html">Empirical 153 Cumulative Distribution Function</a></span></dt> 154<dt><span class="section"><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></span></dt> 155<dt><span class="section"><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value 156 Distribution</a></span></dt> 157<dt><span class="section"><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></span></dt> 158<dt><span class="section"><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and 159 Erlang) Distribution</a></span></dt> 160<dt><span class="section"><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric 161 Distribution</a></span></dt> 162<dt><span class="section"><a href="math_toolkit/dist_ref/dists/hyperexponential_dist.html">Hyperexponential 163 Distribution</a></span></dt> 164<dt><span class="section"><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric 165 Distribution</a></span></dt> 166<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse 167 Chi Squared Distribution</a></span></dt> 168<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse 169 Gamma Distribution</a></span></dt> 170<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse 171 Gaussian (or Inverse Normal) Distribution</a></span></dt> 172<dt><span class="section"><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></span></dt> 173<dt><span class="section"><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic 174 Distribution</a></span></dt> 175<dt><span class="section"><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal 176 Distribution</a></span></dt> 177<dt><span class="section"><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative 178 Binomial Distribution</a></span></dt> 179<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral 180 Beta Distribution</a></span></dt> 181<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral 182 Chi-Squared Distribution</a></span></dt> 183<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F 184 Distribution</a></span></dt> 185<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T 186 Distribution</a></span></dt> 187<dt><span class="section"><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian) 188 Distribution</a></span></dt> 189<dt><span class="section"><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></span></dt> 190<dt><span class="section"><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></span></dt> 191<dt><span class="section"><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></span></dt> 192<dt><span class="section"><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew 193 Normal Distribution</a></span></dt> 194<dt><span class="section"><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students 195 t Distribution</a></span></dt> 196<dt><span class="section"><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular 197 Distribution</a></span></dt> 198<dt><span class="section"><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></span></dt> 199<dt><span class="section"><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></span></dt> 200</dl></dd> 201<dt><span class="section"><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></span></dt> 202</dl></dd> 203<dt><span class="section"><a href="math_toolkit/future.html">Extras/Future Directions</a></span></dt> 204</dl> 205</div> 206</div> 207<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 208<td align="left"></td> 209<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 210 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 211 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 212 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 213 Daryle Walker and Xiaogang Zhang<p> 214 Distributed under the Boost Software License, Version 1.0. (See accompanying 215 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>) 216 </p> 217</div></td> 218</tr></table> 219<hr> 220<div class="spirit-nav"> 221<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> 222</div> 223</body> 224</html> 225
