Estimation of P(Y X) using record values from the generalized inverted exponential distribution

Abstract

This article deals with the estimation of R=P(Y<X), when X and Y are distributed as two independent generalized inverted exponential with common scale parameter and different shape parameters. The maximum likelihood and Bayesian estimators of R are obtained on the basis of upper record values and upper record ranked set samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been achieved using Lindley approximation. Simulation study is performed to compare the reliability estimators in each record sampling scheme with respect to mean squared error.