# Estimating reliability in discrete distributions

• Moon, Yeung-Gil (Department of Tourism Quality Management, Kangwon Tourism College) ;
• Lee, Chang-Soo (Department of Flight Operation, Kyungwoon University)
• Accepted : 2011.06.11
• Published : 2011.08.01

#### Abstract

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.

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