Characterization of Distributions by Moment Relations

Let P(x; θ) be the probability mass function or, probability density function of a random variable X where Using the first k(k≥p) raw or central moments of this distribution we eliminate the p parameters in θ and obtain a moment relation in k moments. We derive the raw and the central moment relations for a number of discrete and continuous distributions. These moment relations are used as criteria to characterize a distribution.