Randomly stopped minima and maxima with exponential-type distributions - Ragulina, Olena; Šiaulys, Jonas (Nonlinear Analysis: Modelling and Control, 2019)
Let ξ1, ξ2,... be a sequence of independent real-valued and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at 0 and integer-valued random variable, which is independent of ξ1, ξ2,.... In this paper, we consider conditions for ξ1, ξ2,... and η under which the distributions of the randomly stopped maxima and minima as well as randomly stopped maxima of sums and randomly stopped minima of sums belong to the class of exponential distributions.