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A gamma variate generator with shape parameter less than unity

Seiji Zenitani

Abstract

Algorithms for generating random numbers that follow a gamma distribution with shape parameter less than unity are proposed. Acceptance-rejection algorithms are developed, based on the generalized exponential distribution. The squeeze technique is applied to our method, and then piecewise envelope functions are further considered. The proposed methods are excellent in acceptance efficiency and promising in speed.

A gamma variate generator with shape parameter less than unity

Abstract

Algorithms for generating random numbers that follow a gamma distribution with shape parameter less than unity are proposed. Acceptance-rejection algorithms are developed, based on the generalized exponential distribution. The squeeze technique is applied to our method, and then piecewise envelope functions are further considered. The proposed methods are excellent in acceptance efficiency and promising in speed.

Paper Structure

This paper contains 6 sections, 27 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Base algorithm
  3. Squeeze technique
  4. Piecewise envelope functions
  5. Numerical tests
  6. Discussion and Summary

Figures (2)

  • Figure 1: Normalized number densities to generate a gamma distribution. Theoretical predictions (curves) and numerical results (circles) are shown, as a function of $\alpha$.
  • Figure 2: (a) Elapsed time to generate $10^8$ gamma variates, including the parameter initialization. (b) Elapsed time to generate $10^8$ gamma variates all at once. See the main text for detail.