Statistical Distributions Tutorial

Boost C++ Libraries

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

This library is centred around statistical distributions, this tutorial will give you an overview of what they are, how they can be used, and provides a few worked examples of applying the library to statistical tests.