Randomly stopped sums with exponential-type distributions
Svetlana Danilenko
Vilnius Gediminas Technical University, Lithuania
Jurgita Markevičiūtė
Vilnius University
Jonas Šiaulys
Vilnius University
Published 2017-10-27


class of exponential distributions
random sum
closure property

How to Cite

Danilenko S., Markevičiūtė J. and Šiaulys J. (2017) “Randomly stopped sums with exponential-type distributions”, Nonlinear Analysis: Modelling and Control, 22(6), pp. 793-807. doi: 10.15388/NA.2017.6.5.


Assume that {ξ1ξ2, …} 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 {ξ1ξ2, …}. In this paper, we consider conditions for η and {ξ1ξ2, …} under which the distribution of the random sum {ξ1 + ξ2 + … + ξη} belongs to the class of exponential distributions.

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