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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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##### References:
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