Gamma Spacings as Finite Gamma Mixtures

Mohamed I. Riffi

Abstract


This paper considers the distributions of spacings between successive order statistics corresponding to a random sample from a two-parameter gamma distribution . We prove that when the shape parameter of the underlying distribution is a positive integer, these spacings can be expressed as finite gamma mixtures. We present exact formulas for computing the distributions of the spacings. Then we present a Mathematica program to implement the results.


Keywords


Gamma distribution, Gamma mixture, Incomplete gamma function, Order statistics, Spacings.

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