Gamma Distribution

The Gamma distribution (the term first used by Weatherburn, 1946) is defined as:

f(x) = (x/b)c-1 * e(-x/b) * [1/bG(c)]

0 <= x, b > 0, c > 0

where

G (gamma)

is the Gamma function

b

is the scale parameter (note: The implementation of the gamma distribution functions for spreadsheet formulas and STATISTICA Visual Basic do not explicitly reference this parameter; to include it in computations involving the gamma(x,c), igamma(x,c), and vgamma(x,c) functions, you can simply rescale x accordingly).

c

is the so-called shape parameter

e

is the base of the natural logarithm, sometimes called Euler's e (2.71...)

Note that while the Gamma distribution (density function) is defined for variate value x=0, the corresponding probability density value is equal to zero. Therefore, the probability of observing a value of 0 is equal to 0, i.e., impossible, and the Gamma distribution cannot be fit to data containing a 0.

The animation above shows the gamma distribution as the shape parameter changes from 1 to 6. For a complete listing of all distribution functions, see Distributions and Their Functions.