Generating Gamma Distributed Variates for Computer Simulation Models

by Morton B. Berman

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback52 pages $20.00 $16.00 20% Web Discount

Compares two methods of generating random variates for simulation studies from gamma distributions with nonintegral shape parameters. The commonly used probability switch approximation method is examined for accuracy and computation costs, while Johnk's exact method is investigated for computation costs. The probability switch method approximates the gamma distribution very closely for shape parameters above 5.0, poorly between 1.0 and 5.0, and not at all below 1.0. Johnk's method, while exact, is 2.5 to 3 times slower in the shape parameter range of 1.0 to 5.0. Johnk's method is recommended for shape parameters below 5.0, and the probability switch method is recommended above 5.0. FORTRAN routines for the two methods are provided. The data used to investigate the accuracy of the probability switch method are appended, as are selected plots of the distributions and a discussion of methods to generate beta variates.

This report is part of the RAND Corporation Report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.