A class of Hurwitz–Lerch Zeta distributions and their applications in reliability

In this paper, we revisit the study of the Hurwitz–Lerch Zeta (HLZ) distribution by investigating its structural properties, reliability properties and statistical inference. More specifically, we explore the reliability properties of the HLZ distribution and investigate the monotonic structure of its failure rate, mean residual life function and the reversed hazard rate. It is shown that the HLZ distribution is log-convex and hence that it is infinitely divisible. Both the hazard rate and the reversed hazard rate are found to be decreasing. The maximum likelihood estimation of the parameters is discussed and an example is provided in which the HLZ distribution fits the data remarkably well.