Modified Power Series Distributions Research Articles

On characterizing distributions by the ration of variance and mean

Recently SAMPSON (1975) has shown that the mean function is enough to characterize the one parameter exponential family. In this paper we consider the class of modified power series distributions introduced by the author (1974) and exhibit a general method of obtaining the distribution if the ratio variance/mean is known. As illustrations characterizations of the POISSON and the geometric distributions are obtained. Considering the continuous version of the exponential family, it is shown that the equality of mean and standard deviation characterizes the exponential distribution.

Maximum Likelihood Estimation of a Modified Power Series Distribution and Some of its Applications

Maximum Likelihood Estimation of a Modified Power Series Distribution and Some of its Applications

Some characterizations of discrete distributions by properties of their moment distributions

The moment distributions of a nonnegative random variable are defined and their applications in life length studies are indicated. Some properties of the moment distributions are employed to characterize the discrete distributions in the class of modified power series distributions introduced by the author (1974). In particular, characterisations of Poisson, binomial and negative binomial distributions are obtained.