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Zbl 1131.62093
Gupta, Pushpa L.; Gupta, Ramesh C.; Ong, Seng-Huat; Srivastava, H.M.
A class of Hurwitz-Lerch zeta distributions and their applications in reliability. (English)
[J] Appl. Math. Comput. 196, No. 2, 521-531 (2008). ISSN 0096-3003

Summary: 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.

MSC 2000:: *62N05 Reliability, etc. (statistics)
62N02 Estimation
62E10 Structure theory of statistical distributions
60E07 Infinitely divisible distributions
62F10 Point estimation

Keywords: modified power series distributions; Hurwitz-Lerch zeta function; log-convex distributions; infinitely divisible distributions; residual life function; reliability functions; hazard rate; reversed hazard rate

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Zentralblatt MATH Berlin [Germany]