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Distributions








General Information:


Other resources (please verify these yourself before using):



The following content is a partial listing of some of the more commonly-recognized probability distributions, both discrete and continuous.


 

DISCRETE DISTRIBUTIONS



Hypergeometric Distribution


General


More information


Binomial Distribution


General


More Information


Negative Binomial Distribution


General


More Information


See also:
  • Pascal distribution
  • Polya distribution


Geometric Distribution


General


More Information


Poisson Distribution


General


More Information



Uniform Distribution (discrete)


General


More Information



 

CONTINUOUS DISTRIBUTIONS


Normal Distribution


Other names: Gaussian Distribution


General


More Information

See also:



Log-normal Distribution


General


More Information



Uniform Distribution (continuous)

Other names: Rectangular Distribution

General
  • Related to the Beta distribution.


More Information



Chi-square Distribution


General
  • Related to the Standard Normal (Z) and Gamma distributions.

More Information



Gamma Distribution


General
  • Related to the Chi-square distribution.

More Information



Beta Distribution


General


More Information



Exponential Distribution


General


More Information



Weibull Distribution


General


More Information


Notes from the R package "survival" ('survreg' function):
  • There are multiple ways to parameterize a Weibull distribution. The survreg function imbeds it in a general location-scale familiy, which is a different parameterization than the rweibull function, and often leads to confusion.
  • survreg's scale = 1/(rweibull shape)
  • survreg's intercept = log(rweibull scale)
  • For the log-likelihood all parameterizations lead to the same value.

The same issues are found in SAS, depending on which procedure is used.  Anyone using software to estimate weibull distribution parameters should be aware of this issue.



Logistic Distribution


General


More Information


F Distribution

General


More Information



Student's t Distribution


General


More Information


R code for graphically comparing the Normal and Student's t distributions is in the file "Compare Normal vs t dist.R" at the bottom of this page.
(Courtesy of Dr. Juan Hu)



Standard Normal (Z) Distribution


General
  • Related to the Chi-square distribution.

More Information
  • NIST - Z Distribution
  • StatSoft - Z Distribution (n/a)
  • Wikipedia - Z Distribution
  • Arsham - Z Distribution

 

 

Other interesting distributions


Cauchy Distribution


General Information
  • An interesting aspect of the Cauchy distribution is that its variance (second moment about the mean) is undefined.

See also:



Rayleigh Distribution


General


More Information



Extreme Value Distribution


General


More Information



Double Exponential (aka Laplace) Distribution


General


More Information



Generalized Gamma Distribution


General


More Information



Gompertz Distribution


General


More Information




Pareto Distribution


General


More Information




Triangular Distribution


General


More Information






ċ
Compare Normal vs t dist.R
(0k)
Clifford Long,
Apr 8, 2014, 8:33 PM
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