On estimating reliability function for the family of power series distribution

Abstract

Explicit expression of the Stress - Strength reliability function, is derived, when the stress (X) and strength (Y) distributions are different members of the Power series family of distributions. Minimum Variance Unbiased (MVU) estimator of R, variance of the MVU estimator together with its MVU estimator are derived for Power series family of distributions. Maximum Likelihood (ML) estimator of R along with related large sample results are also derived. Analytic expressions of the above mentioned quantities are provided for different members of the Power series family of distributions. Further, an application, in the context of real Soccer games, is enumerated.