Characterization of exponential family among a class of density functions by sum of independent random variables

Abstract EN

In this paper we introduce a class of density functions which con-tains some known distributions as non-central X2 and F distributions as wel as all members of the exponential family.

A random sample of size n is taken from a distribution in the given class.

We show that the dis-tribution belongs to exponential family if and only if the sum of the sample elements is sufficient statistic for the natura] parameter.