Maximum likelihood and uniformly minimum variance unbiased estimation of p(y<x) for Gompertz distribution.

Abstract

Maximum likelihood estimator of R = P(Y < X) is derived when all the parameters of Gompertz distribution for X and Y are unknown and unequal. Maximum likelihood estimator for estimating ‘R’ is also derived, when one parameter is known (and equal), but other parameter is unknown for X and Y. Uniformly minimum variance unbiased estimator (UMVUE) of P(Y < X) is also derived for the case when one parameter is known (and unequal), but other parameter is unknown for both X and Y. A new approach has been applied for deriving the UMVUE of R using estimator of power of unknown parameter. Performance of the estimators have been examined using bootstrap technique.