Applying Shrinkage Estimation Technique of P(Y<Max X1, X2,…, Xk) in Case of Generalized Exponential Distribution

Abstract

This paper concerned with estimation reliability (­ for K components parallel system of the stress-strength model with non-identical components which is subjected to a common stress, when the stress and strength follow the Generalized Exponential Distribution (GED) with unknown shape parameter α and the known scale parameter θ (θ=1) to be common. Different shrinkage estimation methods will be considered to estimate ­ depending on maximum likelihood estimator and prior estimates based on simulation using mean squared error (MSE) criteria. The study approved that the shrinkage estimation using shrinkage weight function was the best.

Keywords

• Generalized Exponential Distribution (GED), Stress–Strength (S-S) models, Maximum likelihood estimator (MLE), Shrinkage estimator (Sh) and mean squares error (MSE).