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

f(x) = (x/b)c-1 *

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 |

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.