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Estimation of \(P[Y<X]\) for generalized Pareto distribution. (English) Zbl 1177.62024
Summary: This paper deals with the estimation of \(R=P[Y<X]\) when \(X\) and \(Y\) are two independent generalized Pareto distributions with different parameters. The maximum likelihood estimator and its asymptotic distribution are obtained. An asymptotic confidence interval of \(P[Y<X]\) is constructed using the asymptotic distribution. Assuming that the common scale parameter is known, MLE, UMVUE, Bayes estimation of \(R\) and a confidence interval are obtained. The ML estimator of \(R\), the asymptotic distribution and Bayes estimation of \(R\) in the general case are also studied. Monte Carlo simulations are performed to compare the different proposed methods.

MSC:
62F10 Point estimation
62E20 Asymptotic distribution theory in statistics
62F15 Bayesian inference
62F25 Parametric tolerance and confidence regions
65C05 Monte Carlo methods
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