# 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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