Recurrence relations for moment and conditional moment generating functions of generalized order statistics

Essam K. AL-Hussaini, Abd EL-Baset A. Ahmad and M.A. AL-Kashif

Metrika: International Journal for Theoretical and Applied Statistics, 2005, vol. 61, issue 2, 199-220

Abstract: In this paper, we obtain recurrence relations for moment and conditional moment generating functions of generalized order statistics (gos) based on random samples drawn from a population whose distribution is a member of a doubly truncated class of distributions denoted by [InlineMediaObject not available: see fulltext.]. Members of the class [InlineMediaObject not available: see fulltext.] are characterized in Section (2) based on recurrence relations for moment generating functions (moments) of gos. In Section (3), we shall characterize members of the class [InlineMediaObject not available: see fulltext.] based on recurrence relations for conditional moment generating functions (conditional moments) of gos. These results are specialized to the left, right and non-truncated cases. Ordinary order statistics and ordinary record values are also obtained as special cases of the gos. Characterizations of some members of class [InlineMediaObject not available: see fulltext.] such as the Weibull, compound Weibull, Pareto, power function (beta is a special case), Gompertz and compound Gompertz distributions are given as illustrative examples. Copyright Springer-Verlag 2005

Keywords: Generalized order statistics; ordinary order statistics; ordinary record values (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:61:y:2005:i:2:p:199-220

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DOI: 10.1007/s001840400332

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