# The Real Powers of the Convolution of a Gamma Distribution and a Bernoulli Distribution - Mathematics > Probability

Abstract: In this paper, we essentially compute the set of $x,y>0$ such that themapping $z \longmapsto \Big{}1-r+r e^z\Big{}^x\Big{}\dis\frac{\lambda}{\lambda-z}\Big{}^{y}$ is a Laplace transform. If $X$and $Y$ are two independent random variables which have respectively Bernoulliand Gamma distributions, we denote by $\mu$ the distribution of $X+Y.$ Theabove problem is equivalent to finding the set of $x>0$ such that$\mu^{{\ast}x}$ exists.

Author: Ben Salah Nahla, Masmoudi Afif

Source: https://arxiv.org/