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| 4 | <title>Chapter 5. Statistical Distributions and Functions</title> | |
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| 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> | |
| 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 © 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 Råde, 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>) | |
| 212 | </p> | |
| 213 | </div></td> | |
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