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

Author

Listed:
  • Essam K. AL-Hussaini
  • Abd EL-Baset A. Ahmad
  • M.A. AL-Kashif

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

Suggested Citation

  • Essam K. AL-Hussaini & Abd EL-Baset A. Ahmad & M.A. AL-Kashif, 2005. "Recurrence relations for moment and conditional moment generating functions of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 199-220, April.
    • Handle: RePEc:spr:metrik:v:61:y:2005:i:2:p:199-220
    DOI: 10.1007/s001840400332
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    Cited by:

    1. M. Mahmoud & H. Al-Nagar, 2009. "On generalized order statistics from linear exponential distribution and its characterization," Statistical Papers, Springer, vol. 50(2), pages 407-418, March.

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