Abstract

Lifetime data often come with features that create special problems in the analysis of the data. These features are known as censoring, truncated, grouped, missing and so on. These incomplete problems occur frequently in statistics. In this paper, we introduce a case that contains type I right censoring, left truncated and grouped

data. The likelihood equation is derived for the estimation of the location parameter and the failure rate of a two-parameter exponential distribution under this case. We provide some methods for solving MLE of parameters and a method for handling UMVUE of function of parameters. This function is P(X>=Ta). Finally, these

estimators are compared.

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