Moments of order statistics from the Gompertz-Makeham Distribution

Abstract

In this paper we study the moments of order statistics corresponding to a random sample of finite size from the three-parameter Gompertz-Makeham distribution. We will derive explicit closed-form formulas for the moment-generating function of order statistics from this distribution in terms of the integro-exponential function. Then, we derive explicit close-form formulas for the moments of all orders random variables follow this distribution. Then we prove an identity that relates the moments of order statistics from the Gompertz-Makeham distribution to the moments of random variables from this distribution.