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Chapter 5. Statistical Distributions and Functions

Table of Contents

Statistical Distributions Tutorial

Overview of Statistical Distributions

Headers and Namespaces
Distributions are Objects
Generic operations common to all distributions are non-member functions
Complements are supported too - and when to use them
Parameters can be calculated
Summary

Worked Examples

Distribution Construction Examples

Student's t Distribution Examples

Calculating confidence intervals on the mean with the Students-t distribution
Testing a sample mean for difference from a "true" mean
Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test
Comparing the means of two samples with the Students-t test
Comparing two paired samples with the Student's t distribution

Chi Squared Distribution Examples

Confidence Intervals on the Standard Deviation
Chi-Square Test for the Standard Deviation
Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation

F Distribution Examples

Binomial Distribution Examples

Binomial Coin-Flipping Example
Binomial Quiz Example
Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution
Estimating Sample Sizes for a Binomial Distribution.

Geometric Distribution Examples

Negative Binomial Distribution Examples

Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution
Estimating Sample Sizes for the Negative Binomial.
Negative Binomial Sales Quota Example.
Negative Binomial Table Printing Example.

Normal Distribution Examples

Some Miscellaneous Examples of the Normal (Gaussian) Distribution

Inverse Chi-Squared Distribution Bayes Example

Non Central Chi Squared Example

Tables of the power function of the chi² test.

Error Handling Example

Find Location and Scale Examples

Find Location (Mean) Example
Find Scale (Standard Deviation) Example
Find mean and standard deviation example

Comparison with C, R, FORTRAN-style Free Functions

Using the Distributions from Within C#

Random Variates and Distribution Parameters

Discrete Probability Distributions

Statistical Distributions Reference

Non-Member Properties

Distributions

Arcsine Distribution
Bernoulli Distribution
Beta Distribution
Binomial Distribution
Cauchy-Lorentz Distribution
Chi Squared Distribution
Empirical Cumulative Distribution Function
Exponential Distribution
Extreme Value Distribution
F Distribution
Gamma (and Erlang) Distribution
Geometric Distribution
Holtsmark Distribution
Hyperexponential Distribution
Hypergeometric Distribution
Inverse Chi Squared Distribution
Inverse Gamma Distribution
Inverse Gaussian (or Inverse Normal) Distribution
Kolmogorov-Smirnov Distribution
Landau Distribution
Laplace Distribution
Logistic Distribution
Log Normal Distribution
Map-Airy Distribution
Negative Binomial Distribution
Noncentral Beta Distribution
Noncentral Chi-Squared Distribution
Noncentral F Distribution
Noncentral T Distribution
Normal (Gaussian) Distribution
Pareto Distribution
Poisson Distribution
Rayleigh Distribution
SαS Point5 Distribution
Skew Normal Distribution
Students t Distribution
Triangular Distribution
Uniform Distribution
Weibull Distribution

Distribution Algorithms

Extras/Future Directions

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Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)