Randomly stopped sums with exponential-type distributions - Danilenko, Svetlana; Markevičiūtė, Jurgita; Šiaulys, Jonas (Nonlinear Analysis: Modelling and Control, 2017)
Assume that ξ1, ξ2, … are independent and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at zero and integer-valued random variable, which is independent of ξ1, ξ2, …. In this paper, we consider conditions for η and ξ1, ξ2, … under which the distribution of the random sum ξ1 + ξ2 + … + ξη belongs to the class of exponential distributions.