Common Probability Distributions
This Compendium describes distributions appropriate for the modeling of random data. Although similar summaries may be found in textbooks, this reference exhibits some unusual features, viz.,
- The number of distributions (59) is large, including
- Continuous distributions (37)
-- Symmetric (9)
-- Skewed (27)
- Continuous binary mixtures (11)
- Discrete distributions (6)
- Discrete binary mixtures (6)
- All formulas are shown in their fully-parametrized form, not the standard form.
- Many of the formulas given are seldom described.
- Random variate generation is included where feasible.
- The entire file (1.5Mb, PDF) may be downloaded and printed to give a complete reference book
[but please honor the copyright].
The reason for some of the features listed above is that this Compendium is actually part of the documentation for the Macintosh® freeware package
The latter is a software tool for univariate mathematical modeling and, hence, this Compendium shares the same focus. All of the distributions described here may be used with Regress+ to model empirical data.
Where appropriate, each Compendium entry contains the following items:
- A header giving the distribution name, parameters, and constraints
- A figure showing one or more examples of the PDF
- The formulas for the PDF, CDF and characteristic function (CF)
- The meaning of the parameters and their usual symbols, if any
- Moments, etc., provided closed forms exist
- First Quartile
- Third Quartile
- A formula for generating random variates (inverse-CDF method only)
- Notes regarding constraints, cautions, modeling, etc.
- Aliases and special cases
Click on the link below and select a distribution using the bookmarks.
Compendium of Common Probability Distributions
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