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  25. <div class="chapter">
    26. 

  26. <div class="titlepage"><div><div><h1 class="title">
    27. 

  27. <a name="dist"></a>Chapter&#160;5.&#160;Statistical Distributions and Functions</h1></div></div></div>
    28. 

  28. <div class="toc">
    29. 

  29. <p><b>Table of Contents</b></p>
    30. 

  30. <dl class="toc">
    31. 

  31. <dt><span class="section"><a href="math_toolkit/stat_tut.html">Statistical Distributions Tutorial</a></span></dt>
    32. 

  32. <dd><dl>
    33. 

  33. <dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Statistical
    34. 

  34.       Distributions</a></span></dt>
    35. 

  35. <dd><dl>
    36. 

  36. <dt><span class="section"><a href="math_toolkit/stat_tut/overview/headers.html">Headers and
    37. 

  37.         Namespaces</a></span></dt>
    38. 

  38. <dt><span class="section"><a href="math_toolkit/stat_tut/overview/objects.html">Distributions
    39. 

  39.         are Objects</a></span></dt>
    40. 

  40. <dt><span class="section"><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations
    41. 

  41.         common to all distributions are non-member functions</a></span></dt>
    42. 

  42. <dt><span class="section"><a href="math_toolkit/stat_tut/overview/complements.html">Complements
    43. 

  43.         are supported too - and when to use them</a></span></dt>
    44. 

  44. <dt><span class="section"><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters
    45. 

  45.         can be calculated</a></span></dt>
    46. 

  46. <dt><span class="section"><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></span></dt>
    47. 

  47. </dl></dd>
    48. 

  48. <dt><span class="section"><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></span></dt>
    49. 

  49. <dd><dl>
    50. 

  50. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution
    51. 

  51.         Construction Examples</a></span></dt>
    52. 

  52. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution
    53. 

  53.         Examples</a></span></dt>
    54. 

  54. <dd><dl>
    55. 

  55. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating
    56. 

  56.           confidence intervals on the mean with the Students-t distribution</a></span></dt>
    57. 

  57. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html">Testing
    58. 

  58.           a sample mean for difference from a "true" mean</a></span></dt>
    59. 

  59. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html">Estimating
    60. 

  60.           how large a sample size would have to become in order to give a significant
    61. 

  61.           Students-t test result with a single sample test</a></span></dt>
    62. 

  62. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html">Comparing
    63. 

  63.           the means of two samples with the Students-t test</a></span></dt>
    64. 

  64. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/paired_st.html">Comparing
    65. 

  65.           two paired samples with the Student's t distribution</a></span></dt>
    66. 

  66. </dl></dd>
    67. 

  67. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution
    68. 

  68.         Examples</a></span></dt>
    69. 

  69. <dd><dl>
    70. 

  70. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence
    71. 

  71.           Intervals on the Standard Deviation</a></span></dt>
    72. 

  72. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square
    73. 

  73.           Test for the Standard Deviation</a></span></dt>
    74. 

  74. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html">Estimating
    75. 

  75.           the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></span></dt>
    76. 

  76. </dl></dd>
    77. 

  77. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></span></dt>
    78. 

  78. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution
    79. 

  79.         Examples</a></span></dt>
    80. 

  80. <dd><dl>
    81. 

  81. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial
    82. 

  82.           Coin-Flipping Example</a></span></dt>
    83. 

  83. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial
    84. 

  84.           Quiz Example</a></span></dt>
    85. 

  85. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_conf.html">Calculating
    86. 

  86.           Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></span></dt>
    87. 

  87. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating
    88. 

  88.           Sample Sizes for a Binomial Distribution.</a></span></dt>
    89. 

  89. </dl></dd>
    90. 

  90. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution
    91. 

  91.         Examples</a></span></dt>
    92. 

  92. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial
    93. 

  93.         Distribution Examples</a></span></dt>
    94. 

  94. <dd><dl>
    95. 

  95. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating
    96. 

  96.           Confidence Limits on the Frequency of Occurrence for the Negative Binomial
    97. 

  97.           Distribution</a></span></dt>
    98. 

  98. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
    99. 

  99.           Sample Sizes for the Negative Binomial.</a></span></dt>
    100. 

  100. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative
    101. 

  101.           Binomial Sales Quota Example.</a></span></dt>
    102. 

  102. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative
    103. 

  103.           Binomial Table Printing Example.</a></span></dt>
    104. 

  104. </dl></dd>
    105. 

  105. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution
    106. 

  106.         Examples</a></span></dt>
    107. 

  107. <dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example/normal_misc.html">Some
    108. 

  108.           Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
    109. 

  109. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse
    110. 

  110.         Chi-Squared Distribution Bayes Example</a></span></dt>
    111. 

  111. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi
    112. 

  112.         Squared Example</a></span></dt>
    113. 

  113. <dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables
    114. 

  114.           of the power function of the chi<sup>2</sup> test.</a></span></dt></dl></dd>
    115. 

  115. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling
    116. 

  116.         Example</a></span></dt>
    117. 

  117. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and
    118. 

  118.         Scale Examples</a></span></dt>
    119. 

  119. <dd><dl>
    120. 

  120. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_location_eg.html">Find
    121. 

  121.           Location (Mean) Example</a></span></dt>
    122. 

  122. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html">Find
    123. 

  123.           Scale (Standard Deviation) Example</a></span></dt>
    124. 

  124. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find
    125. 

  125.           mean and standard deviation example</a></span></dt>
    126. 

  126. </dl></dd>
    127. 

  127. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with
    128. 

  128.         C, R, FORTRAN-style Free Functions</a></span></dt>
    129. 

  129. <dt><span class="section"><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions
    130. 

  130.         from Within C#</a></span></dt>
    131. 

  131. </dl></dd>
    132. 

  132. <dt><span class="section"><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution
    133. 

  133.       Parameters</a></span></dt>
    134. 

  134. <dt><span class="section"><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability
    135. 

  135.       Distributions</a></span></dt>
    136. 

  136. </dl></dd>
    137. 

  137. <dt><span class="section"><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></span></dt>
    138. 

  138. <dd><dl>
    139. 

  139. <dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt>
    140. 

  140. <dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt>
    141. 

  141. <dd><dl>
    142. 

  142. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/arcine_dist.html">Arcsine Distribution</a></span></dt>
    143. 

  143. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli
    144. 

  144.         Distribution</a></span></dt>
    145. 

  145. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt>
    146. 

  146. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial
    147. 

  147.         Distribution</a></span></dt>
    148. 

  148. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
    149. 

  149.         Distribution</a></span></dt>
    150. 

  150. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared
    151. 

  151.         Distribution</a></span></dt>
    152. 

  152. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/empirical_cdf.html">Empirical
    153. 

  153.         Cumulative Distribution Function</a></span></dt>
    154. 

  154. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></span></dt>
    155. 

  155. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value
    156. 

  156.         Distribution</a></span></dt>
    157. 

  157. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></span></dt>
    158. 

  158. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and
    159. 

  159.         Erlang) Distribution</a></span></dt>
    160. 

  160. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric
    161. 

  161.         Distribution</a></span></dt>
    162. 

  162. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/hyperexponential_dist.html">Hyperexponential
    163. 

  163.         Distribution</a></span></dt>
    164. 

  164. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
    165. 

  165.         Distribution</a></span></dt>
    166. 

  166. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
    167. 

  167.         Chi Squared Distribution</a></span></dt>
    168. 

  168. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse
    169. 

  169.         Gamma Distribution</a></span></dt>
    170. 

  170. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse
    171. 

  171.         Gaussian (or Inverse Normal) Distribution</a></span></dt>
    172. 

  172. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></span></dt>
    173. 

  173. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic
    174. 

  174.         Distribution</a></span></dt>
    175. 

  175. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal
    176. 

  176.         Distribution</a></span></dt>
    177. 

  177. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative
    178. 

  178.         Binomial Distribution</a></span></dt>
    179. 

  179. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral
    180. 

  180.         Beta Distribution</a></span></dt>
    181. 

  181. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
    182. 

  182.         Chi-Squared Distribution</a></span></dt>
    183. 

  183. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F
    184. 

  184.         Distribution</a></span></dt>
    185. 

  185. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T
    186. 

  186.         Distribution</a></span></dt>
    187. 

  187. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian)
    188. 

  188.         Distribution</a></span></dt>
    189. 

  189. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></span></dt>
    190. 

  190. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></span></dt>
    191. 

  191. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></span></dt>
    192. 

  192. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew
    193. 

  193.         Normal Distribution</a></span></dt>
    194. 

  194. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students
    195. 

  195.         t Distribution</a></span></dt>
    196. 

  196. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular
    197. 

  197.         Distribution</a></span></dt>
    198. 

  198. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></span></dt>
    199. 

  199. <dt><span class="section"><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></span></dt>
    200. 

  200. </dl></dd>
    201. 

  201. <dt><span class="section"><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></span></dt>
    202. 

  202. </dl></dd>
    203. 

  203. <dt><span class="section"><a href="math_toolkit/future.html">Extras/Future Directions</a></span></dt>
    204. 

  204. </dl>
    205. 

  205. </div>
    206. 

  206. </div>
    207. 

  207. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    208. 

  208. <td align="left"></td>
    209. 

  209. <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
    210. 

  210.       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
    211. 

  211.       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
    212. 

  212.       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
    213. 

  213.       Daryle Walker and Xiaogang Zhang<p>
    214. 

  214.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    215. 

  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. 

  216.       </p>
    217. 

  217. </div></td>
    218. 

  218. </tr></table>
    219. 

  219. <hr>
    220. 

  220. <div class="spirit-nav">
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