Inference on Positive Exponential Family of Distributions (PEFD) through Transformation Method
The estimation of R(t) and R = Pr(Y > X) for the Positive Exponential Family of Distribution
(PEFD) is considered. The UMVUE's, MLE's and Confidence Interval are derived.
These estimators are derived through the method of Transformation. The α = P(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.