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Estimation of \(P(Y<X)\) for the three-parameter generalized exponential distribution. (English) Zbl 1292.62041
Summary: This article considers the estimation of \(R=P(Y<X)\) when \(X\) and \(Y\) are distributed as two independent three-parameter generalized exponential (GE) random variables with different shape parameters but having the same location and scale parameters. A modified maximum likelihood method and a Bayesian technique are used to estimate \(R\) on the basis of independent complete samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been determined using an importance sampling procedure. An analysis of a real life data set is presented for illustrative purposes.

MSC:
62F10 Point estimation
62F15 Bayesian inference
62G30 Order statistics; empirical distribution functions
62F25 Parametric tolerance and confidence regions
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