Bounds of moment generating functions of some life distributions

    Authors

    I. A. Ahmad;A. R. Mugdadi

    Comments

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    Abbreviated Journal Title

    Stat. Pap.

    Keywords

    life distributions; moment generating functions; Laplace transformation; Poisson shock model; residual life time; stationary life time; RENEWAL; Statistics & Probability

    Abstract

    In this article we show that if a life has new better than used in expectation (NBUE) ageing property and if the mean life is finite then the moment generating function exists and is finite. In fact, the moment generating function is shown to be bounded above by that of the exponential distribution with the same mean. Analogous results are also proven for two much bigger families of life distribution, namely, the new better than renewal used in expectation (NBRUE) and the renewal new is better than used in expectation (RNBUE) and the renewal new better than renewal used in expectation (RNBRUE), provided that the life has finite two moments. Further, stronger results are also obtained for the smaller new better than used version of the above classes.

    Journal Title

    Statistical Papers

    Volume

    46

    Issue/Number

    4

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    575

    Last Page

    585

    WOS Identifier

    WOS:000232138600006

    ISSN

    0932-5026

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