Distributions of Gamma m-Spacings

Abstract

This paper is concerned with the distributions of the -spacings of order statistics associated with a sample from a two-parameter gamma population when the shape parameter is a positive integer. We prove that the -spacings have finite mixture distributions with negative components, each of which in turn has a finite gamma mixture distribution. We write the probability density function of the -spacings in closed form and provide a Mathematica code for the implementation.