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<div class="chapter">
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<div class="titlepage"><div><div><h1 class="title">
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<a name="dist"></a>Chapter 5. Statistical Distributions and Functions</h1></div></div></div>
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<div class="toc">
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<p><b>Table of Contents</b></p>
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<dl class="toc">
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<dt><span class="section"><a href="math_toolkit/stat_tut.html">Statistical Distributions Tutorial</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Statistical
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Distributions</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview/headers.html">Headers and
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Namespaces</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview/objects.html">Distributions
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are Objects</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations
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common to all distributions are non-member functions</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview/complements.html">Complements
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are supported too - and when to use them</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters
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can be calculated</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution
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Construction Examples</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution
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Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating
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confidence intervals on the mean with the Students-t distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html">Testing
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a sample mean for difference from a "true" mean</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html">Estimating
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how large a sample size would have to become in order to give a significant
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Students-t test result with a single sample test</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html">Comparing
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the means of two samples with the Students-t test</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg/paired_st.html">Comparing
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two paired samples with the Student's t distribution</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution
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Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence
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Intervals on the Standard Deviation</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square
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Test for the Standard Deviation</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html">Estimating
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the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution
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Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial
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Coin-Flipping Example</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial
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Quiz Example</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_conf.html">Calculating
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Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating
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Sample Sizes for a Binomial Distribution.</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution
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Examples</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial
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Distribution Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating
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Confidence Limits on the Frequency of Occurrence for the Negative Binomial
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
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Sample Sizes for the Negative Binomial.</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative
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Binomial Sales Quota Example.</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative
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Binomial Table Printing Example.</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution
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Examples</a></span></dt>
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<dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example/normal_misc.html">Some
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Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse
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Chi-Squared Distribution Bayes Example</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi
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Squared Example</a></span></dt>
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<dd><dl><dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables
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of the power function of the chi<sup>2</sup> test.</a></span></dt></dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling
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Example</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and
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Scale Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_location_eg.html">Find
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Location (Mean) Example</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html">Find
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Scale (Standard Deviation) Example</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find
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mean and standard deviation example</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with
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C, R, FORTRAN-style Free Functions</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions
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from Within C#</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution
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Parameters</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability
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Distributions</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/arcine_dist.html">Arcsine Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/empirical_cdf.html">Empirical
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Cumulative Distribution Function</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and
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Erlang) Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/hyperexponential_dist.html">Hyperexponential
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
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Chi Squared Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse
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Gamma Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse
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Gaussian (or Inverse Normal) Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/kolmogorov_smirnov_dist.html">Kolmogorov-Smirnov
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative
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Binomial Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral
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Beta Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
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Chi-Squared Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian)
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew
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Normal Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students
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t Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular
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Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></span></dt>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></span></dt>
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</dl></dd>
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<dt><span class="section"><a href="math_toolkit/future.html">Extras/Future Directions</a></span></dt>
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</dl>
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</div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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