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   4 <title>Chapter&#160;5.&#160;Statistical Distributions and Functions</title>
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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>
  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 Distributions</a></span></dt>
  34 <dd><dl>
  35 <dt><span class="section"><a href="math_toolkit/stat_tut/overview/headers.html">Headers and
  36         Namespaces</a></span></dt>
  37 <dt><span class="section"><a href="math_toolkit/stat_tut/overview/objects.html">Distributions
  38         are Objects</a></span></dt>
  39 <dt><span class="section"><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations
  40         common to all distributions are non-member functions</a></span></dt>
  41 <dt><span class="section"><a href="math_toolkit/stat_tut/overview/complements.html">Complements
  42         are supported too - and when to use them</a></span></dt>
  43 <dt><span class="section"><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters
  44         can be calculated</a></span></dt>
  45 <dt><span class="section"><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></span></dt>
  46 </dl></dd>
  47 <dt><span class="section"><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></span></dt>
  48 <dd><dl>
  49 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution
  50         Construction Examples</a></span></dt>
  51 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution
  52         Examples</a></span></dt>
  53 <dd><dl>
  54 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating
  55           confidence intervals on the mean with the Students-t distribution</a></span></dt>
  56 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html">Testing
  57           a sample mean for difference from a "true" mean</a></span></dt>
  58 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html">Estimating
  59           how large a sample size would have to become in order to give a significant
  60           Students-t test result with a single sample test</a></span></dt>
  61 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html">Comparing
  62           the means of two samples with the Students-t test</a></span></dt>
  63 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/paired_st.html">Comparing
  64           two paired samples with the Student's t distribution</a></span></dt>
  65 </dl></dd>
  66 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution
  67         Examples</a></span></dt>
  68 <dd><dl>
  69 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence
  70           Intervals on the Standard Deviation</a></span></dt>
  71 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square
  72           Test for the Standard Deviation</a></span></dt>
  73 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html">Estimating
  74           the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></span></dt>
  75 </dl></dd>
  76 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></span></dt>
  77 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution
  78         Examples</a></span></dt>
  79 <dd><dl>
  80 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial
  81           Coin-Flipping Example</a></span></dt>
  82 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial
  83           Quiz Example</a></span></dt>
  84 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_conf.html">Calculating
  85           Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></span></dt>
  86 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating
  87           Sample Sizes for a Binomial Distribution.</a></span></dt>
  88 </dl></dd>
  89 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution
  90         Examples</a></span></dt>
  91 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial
  92         Distribution Examples</a></span></dt>
  93 <dd><dl>
  94 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating
  95           Confidence Limits on the Frequency of Occurrence for the Negative Binomial
  96           Distribution</a></span></dt>
  97 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
  98           Sample Sizes for the Negative Binomial.</a></span></dt>
  99 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative
 100           Binomial Sales Quota Example.</a></span></dt>
 101 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative
 102           Binomial Table Printing Example.</a></span></dt>
 103 </dl></dd>
 104 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution
 105         Examples</a></span></dt>
 106 <dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example/normal_misc.html">Some
 107           Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
 108 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse
 109         Chi-Squared Distribution Bayes Example</a></span></dt>
 110 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi
 111         Squared Example</a></span></dt>
 112 <dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables
 113           of the power function of the chi<sup>2</sup> test.</a></span></dt></dl></dd>
 114 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling
 115         Example</a></span></dt>
 116 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and
 117         Scale Examples</a></span></dt>
 118 <dd><dl>
 119 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_location_eg.html">Find
 120           Location (Mean) Example</a></span></dt>
 121 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html">Find
 122           Scale (Standard Deviation) Example</a></span></dt>
 123 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find
 124           mean and standard deviation example</a></span></dt>
 125 </dl></dd>
 126 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with
 127         C, R, FORTRAN-style Free Functions</a></span></dt>
 128 <dt><span class="section"><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions
 129         from Within C#</a></span></dt>
 130 </dl></dd>
 131 <dt><span class="section"><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution
 132       Parameters</a></span></dt>
 133 <dt><span class="section"><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability
 134       Distributions</a></span></dt>
 135 </dl></dd>
 136 <dt><span class="section"><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></span></dt>
 137 <dd><dl>
 138 <dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt>
 139 <dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt>
 140 <dd><dl>
 141 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/arcine_dist.html">Arcsine Distribution</a></span></dt>
 142 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli
 143         Distribution</a></span></dt>
 144 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt>
 145 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial
 146         Distribution</a></span></dt>
 147 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
 148         Distribution</a></span></dt>
 149 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared
 150         Distribution</a></span></dt>
 151 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></span></dt>
 152 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value
 153         Distribution</a></span></dt>
 154 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></span></dt>
 155 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and
 156         Erlang) Distribution</a></span></dt>
 157 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric
 158         Distribution</a></span></dt>
 159 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/hyperexponential_dist.html">Hyperexponential
 160         Distribution</a></span></dt>
 161 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
 162         Distribution</a></span></dt>
 163 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
 164         Chi Squared Distribution</a></span></dt>
 165 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse
 166         Gamma Distribution</a></span></dt>
 167 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse
 168         Gaussian (or Inverse Normal) Distribution</a></span></dt>
 169 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></span></dt>
 170 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic
 171         Distribution</a></span></dt>
 172 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal
 173         Distribution</a></span></dt>
 174 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative
 175         Binomial Distribution</a></span></dt>
 176 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral
 177         Beta Distribution</a></span></dt>
 178 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
 179         Chi-Squared Distribution</a></span></dt>
 180 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F
 181         Distribution</a></span></dt>
 182 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T
 183         Distribution</a></span></dt>
 184 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian)
 185         Distribution</a></span></dt>
 186 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></span></dt>
 187 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></span></dt>
 188 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></span></dt>
 189 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew
 190         Normal Distribution</a></span></dt>
 191 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students
 192         t Distribution</a></span></dt>
 193 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular
 194         Distribution</a></span></dt>
 195 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></span></dt>
 196 <dt><span class="section"><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></span></dt>
 197 </dl></dd>
 198 <dt><span class="section"><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></span></dt>
 199 </dl></dd>
 200 <dt><span class="section"><a href="math_toolkit/future.html">Extras/Future Directions</a></span></dt>
 201 </dl>
 202 </div>
 203 </div>
 204 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 205 <td align="left"></td>
 206 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 207       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 208       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 209       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 210         Distributed under the Boost Software License, Version 1.0. (See accompanying
 211         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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