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Estimation of P[ \(Y < X ]\) for generalized exponential distribution. (English) Zbl 1079.62032
Summary: This paper deals with the estimation of \(P[Y<X]\) when \(X\) and \(Y\) are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of \(P[Y<X]\). Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of \(P[Y<X]\) are obtained. Different confidence intervals are proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a simulated data set has also been presented for illustrative purposes.

MSC:
62F10 Point estimation
62E20 Asymptotic distribution theory in statistics
62F25 Parametric tolerance and confidence regions
62F15 Bayesian inference
65C05 Monte Carlo methods
62N05 Reliability and life testing
62F40 Bootstrap, jackknife and other resampling methods
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