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 (56) is large, including
- Continuous distributions (30)
-- Symmetric (11)
-- Skewed (19)
- Continuous binary mixtures (17)
- Discrete distributions (5)
- Discrete binary mixtures (4)
- 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.
- Each (two-page) entry is readily printable in full 600-dpi resolution (see below), and/or
- The entire file (549K, pdf) may be downloaded and printed to give a complete reference book
[but please honor the copyright].
Data Modeling
The reason for most of the features listed above is that this reference is actually Appendix A from the documentation accompanying the Macintosh® freeware package
Regress+
The latter is a software tool for 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.
A general, introductory Tutorial on mathematical modeling (pdf) is available
here.
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 and CDF
- The meaning of the parameters and their usual symbols, if any
- Moments, etc., provided closed forms exist
- Mean
- Variance
- Skewness (dimensionless)
- Kurtosis (dimensionless, and relative to the Normal distribution)
- Mode
- Median
- First Quartile
- Third Quartile
- qMean (Quantile of the Mean)
- qMode (Quantile of the Mode)
- 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.
[Requires the free Adobe Acrobat® Reader plug-in. If you don't have it, then your browser should be updated! Alternatively, or if the plug-in does not work, change your browser preferences to use Acrobat Reader instead.]
A Compendium of Common Probability Distributions
Printing Notes
Compendium entries are intended to be printed on a PostScript® printer at 600-dpi resolution (or higher). The file, as a whole, is formatted to be reproduced double-sided. In addition, the following settings/options should be checked:
- In Adobe Acrobat, make sure that the image is set to Actual Size (100%).
- In Adobe Acrobat, in the Print dialog under Acrobat options (in dropdown menu), make sure that Fit to Page is OFF.
- In the Page Setup dialog, the paper size should be set to US Letter with scale at 100%.
Note: Some of the terms above are Macintosh descriptors; Windows users should translate accordingly.
These printing notes also apply to the Tutorial cited above.
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