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Bounds of moment generating functions of some life distributions

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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.

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Central Florida, 32816, Orlando, FL, USA

    Ibrahim A. Ahmad

  2. Department of Mathematics, Southern Illinois University, 62901, Carbondale, IL, USA

    A. R. Mugdadi

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  1. Ibrahim A. Ahmad
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  2. A. R. Mugdadi
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Ahmad, I.A., Mugdadi, A.R. Bounds of moment generating functions of some life distributions. Statistical Papers 46, 575–585 (2005). https://doi.org/10.1007/BF02763006

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  • DOI: https://doi.org/10.1007/BF02763006

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