Common Probability Distributions

This Compendium describes distributions appropriate for modeling "random" observations. 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].

Data Modeling

The distributions in this Compendium are typically used to model data of various kinds. The best, state-of-the-art way to carry out that process is via Bayesian inference, fully explained in the ebook Data, Uncertainty and Inference and implemented in the Mac OS X™ application MacMCMC

Both of these offerings are completely free and will remain so.

Included Items

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
- Mean
- Variance
- Skewness
- Kurtosis
- Mode
- Median
- First Quartile
- Third Quartile
A formula for generating random variates (inverse-CDF method only)
Notes regarding constraints, cautions, modeling, etc.
Aliases and special cases
Characterizations

Click on the link below and select a distribution using the bookmarks.

Compendium of Common Probability Distributions

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