Random convolution of O-exponential distributions

Abstract

Assume that ξ1, ξ2, ... are independent and identically distributed non-negative random variables having the O-exponential distribution. Suppose that η is a nonnegative non-degenerate at zero integer-valued random variable independent of ξ1, ξ2, ... . In this paper, we consider the conditions for η under which the distribution of random sum ξ1 + ξ2 + ... + ξη remains in the class of O-exponential distributions.

Keywords

• ong tail
• random sum
• closure property
• O-exponential distribution