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- W333864406 abstract "Abstract We shall introduce a general probability mass function which includes several dis-crete probability mass functions. Especially, when the random variable X is Poisson,binomial, and negative binomial random variables as some special cases of the in-troduced distribution, the maximum likelihood estimator (MLE) and the uniformlyminimum variance unbiased estimator (UMVUE) of the probability P(X t) areconsidered. And the eciencies of the MLE and the UMVUE of the reliability arecompared each other.Keywords: Binomial, maximum likelihood estimator, negative binomial, Poisson, uni-formly minimum variance unbiased estimator. 1. Introduction Many authors have considered a right tail probability in continuous distributions for thereliability theory. Lee and Won (2006) considered inference on reliability in an exponentiateduniform distribution. Woo (2007, 2008) studied a reliability in two independent half normaldistributions and Levy-uniform distributions. Moon and Lee (2009) considered an inferenceon the reliability in two independent gamma random variables. Lee and Lee (2010) con-sidered reliability in two independent right truncated Rayleigh distributions. Ali and Woo(2010) studied estimation of tail probability and reliability in exponentiated Pareto case.Since the curtate future lifetime random variable X has non-negative integer values, it isnatural in actuarial studies to consider the right tail probability of discrete random variablesto apply a reliability to evaluation of life insurance premiums (see, Bowers et al., 1997).Because reliability R(t) = P(X>t) = 1 P(Xt) is a monotone function of P(Xt),an inference on the reliability is equivalent to an inference on P(Xt) in McCool (1991),and hence instead of an inference on the reliability, it’s sucient for us to consider aninference on P(Xt) .In this paper, We introduce a general probability mass function which includes severaldiscrete probability mass functions. Especially, when the random variable X is Poisson,binomial, and negative binomial random variables as some special cases of the introduceddistribution, the MLE and the UMVUE of the probability P(Xt) are considered. Andthe eciencies of the MLE and the UMVUE of the reliability are compared each other." @default.
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- W333864406 date "2011-01-01" @default.
- W333864406 modified "2023-09-24" @default.
- W333864406 title "Estimating reliability in discrete distributions" @default.
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