Saxena, Ram K.; Pogány, Tibor K.; Saxena, Ravi; Jankov, Dragana On generalized Hurwitz-Lerch zeta distributions occuring in statistical inference. (English) Zbl 1268.11127 Acta Univ. Sapientiae, Math. 3, No. 1, 43-59 (2011). Summary: The object of the present paper is to define certain new incomplete generalized Hurwitz-Lerch zeta functions and incomplete generalized Gamma functions. Further, we introduce two new statistical distributions named as, generalized Hurwitz-Lerch zeta Beta prime distribution and generalized Hurwitz-Lerch zeta Gamma distribution and investigate their statistical functions, such as moments, distribution and survivor function, characteristic function, the hazard rate function and the mean residue life functions. Finally, moment method parameter estimators are given by means of a statistical sample of size \(n\). The results obtained provide an elegant extension of the work reported earlier by M. Garg et al. [Appl. Appl. Math. 4, No. 1, 26–39 (2009; Zbl 1186.11055)] and others. Cited in 5 Documents MSC: 11M35 Hurwitz and Lerch zeta functions 33C05 Classical hypergeometric functions, \({}_2F_1\) 60E05 Probability distributions: general theory 60E10 Characteristic functions; other transforms Keywords:Riemann zeta function; Lerch zeta function; Hurwitz-Lerch zeta function; hazard function; mean residual life function; characteristic function; Planck distribution; generalized Beta prime distribution; moment method parameter estimation Citations:Zbl 1186.11055 PDFBibTeX XMLCite \textit{R. K. Saxena} et al., Acta Univ. Sapientiae, Math. 3, No. 1, 43--59 (2011; Zbl 1268.11127) Full Text: EMIS