A Robust Estimator of R = P(X > Y ) of Heavy-tailed Distributions and its Sampling Distributions

摘要

Heavy-tailed distributions have wide applications in life-time contexts, especially in reliability and risk modeling. So we consider the estimation problem of reliability, R = P(X > Y ) for small samples, when X and Y are two independent but not identically distributed random variables belonging to the family of heavy-tailed distributions, using a robust estimator, namely the harmonic moment estimator. Extensive simulation studies are carried out to study the performance of this estimator. The relative efficiency of the estimator with the well known Hill estimator is studied. We obtain the sampling distribution of the parameters of the distribution as well as that of estimator of R which will help us to study the properties of the estimators. Also we find out the asymptotic confidence intervals of R and its performance is studied with respect to average width and the coverage probability, through simulations.