Identities Based on Probability Mass Functions

Abstract

Moments of discrete distributions are usually calculated by averaging the probability mass function or calculating characteristic function and then differentiating it. In this paper we try to popularize a mass identity technique for calculating moments. Since the probability mass function adds to one, an identity called mass identity or density identity is obtained. Differentiating repeatedly by a continuous parameter in the density identity, we obtain higher order mass identities that may be useful beyond the calculation of moments.