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  26 <div class="titlepage"><div><div><h1 class="title">
  27 <a name="dist"></a>Chapter&#160;5.&#160;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 &#169; 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       R&#229;de, 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>
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