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Estimation of $$R=P(Y<X)$$ for three-parameter Weibull distribution. (English) Zbl 1169.62012
Summary: We consider the estimation of the stress-strength parameter $$R=P(Y<X)$$, when $$X$$ and $$Y$$ are independent and both are three-parameter Weibull distributions with common shape and location parameters but different scale parameters. It is observed that the maximum likelihood estimators do not exist in this case, and we propose a modified maximum likelihood estimator, and also an approximate modified maximum likelihood estimator of $$R$$. We obtain the asymptotic distribution of the modified maximum likelihood estimators of the unknown parameters which can be used to construct confidence interval of $$R$$. Analyses of two data sets have also been presented for illustrative purposes.

##### MSC:
 62F10 Point estimation 62E20 Asymptotic distribution theory in statistics 62N05 Reliability and life testing 62N02 Estimation in survival analysis and censored data
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##### References:
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