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Comparison of different estimators of $$P[Y<X]$$ for a scaled Burr type $$X$$ distribution. (English) Zbl 1065.62172
Summary: We consider the estimation of $$P[Y < X]$$ when $$Y$$ and $$X$$ are two independent scaled Burr Type $$X$$ distributions having the same scale parameter. The maximum likelihood estimator and its asymptotic distribution are 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 approximate Bayes estimators of $$P[Y < X]$$ are discussed. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulations. One data set has been analyzed for illustrative purposes.

##### MSC:
 62N02 Estimation in survival analysis and censored data 65C05 Monte Carlo methods 62F25 Parametric tolerance and confidence regions 62F10 Point estimation 62E20 Asymptotic distribution theory in statistics 62F15 Bayesian inference 65C60 Computational problems in statistics (MSC2010)
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