Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

GAMMA distribution

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_374

A continuous random variable is said to have a gamma distribution if its probability density can be written in the form f(t) = a(at)b−1eat/Γ(b) where a and b are any positive real numbers and Γ(b) is the gamma function evaluated at b. The constant b is called the shape parameter, while a (or various equivalents) is called the scale parameter. If b happens to be a positive integer, then Γ (b) = (b − 1)! and this gamma distribution is also called an Erlang distribution. Furthermore, if b is either an integer or half-integer (1/2, 3/2, etc.) and a = 1/2, the resultant gamma distribution is equivalent to the classical χ2 distribution of statistics.  Erlang distribution.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA