Inference on Positive Exponential Family of Distributions (PEFD) through Transformation Method

Abstract

The estimation of R(t) and R=Pr(Y>X) for the Positive Exponential Family of Distribution (PEFD) is considered. The UMVUES, MLES and Confidence Interval are derived. These estimators are derived through the method of Transformation. The α=Pr(X>γ), which is termed as probability of disaster is also derived when random stress X follows PEFD and finite strength follows Power function distribution.