(1) School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China
Abstract:
In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special
cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution
function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model
and the reliability of a two-unit cold standby system in reliability theory.