On the powers of Kummer distribution

Abstract

The Kummer distribution is a probability distribution, whose density is given by where and is a normalizing constant. In this paper, the distributions of random variable where has the Kummer distribution, are considered with the conditions being IFR/DFR, some properties of moments depending on the parameters and the moment-(in)determinacy. In the case of moment-indeterminacy, exemplary Stieltjes classes are constructed.