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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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##### References:
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