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

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• 作者：Pushpa L. Gupta ; Ramesh C. Gupta ; Seng-Huat Ong ; H.M. Srivastava
• 关键词：Modified power series distributions ; Hurwitz– ; Lerch Zeta function ; Log– ; convex distributions ; Statistical inference ; Infinitely divisible distributions ; Residual life function ; Reliability functions ; Hazard rate ; Reversed hazard rate
• 刊名：Applied Mathematics and Computation
• 出版年：2008
• 出版时间：1 March 2008
• 年：2008
• 卷：196
• 期：2
• 页码：521-531
• 全文大小：168 K

文摘

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.