Simulation of truncated and unimodal gamma distributions

Abstract

An efficient random variable generator for a truncated gamma distribution with shape parameter greater than 1 is designed using an acceptance-rejection algorithm. Based on an approximation to a transformed gamma density function by the standard normal density, numerical information for the standard normal density is prepared in advance, and the calculation is performed with reference to that information. An improvement via a squeezing method is proposed to reduce the computational burden and time. The algorithm's acceptance rate for generating truncated gamma variables is very high and almost 1 when the truncated distribution is unimodal. Numerical experiments for one- and two-sided truncated domain cases are conducted to measure the execution time, including the parameter setup time. Compared with existing truncated gamma variate generators, the proposed method performs better when the distribution is unimodal and the shape parameter is equal to or greater than 3.3.

Keywords:

• Acceptance-rejection algorithm
• shape parameter
• squeezing
• truncated gamma distribution

Mathematics Subject Classifications:

• 65C05
• 65C10
• 62-08

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by JSPS KAKENHI Grant Numbers JP19H00588 and JP20K19751.