Abstract
SYNOPTIC ABSTRACTThis article deals with the estimation of R = P(Y < X) when X and Y are two independent random variables following inverse Pareto distributions with different parameters. The maximum-likelihood estimator of R and its asymptotic sampling distribution are proposed. The asymptotic sampling distribution is used to construct an asymptotic confidence interval for R. The exact confidence interval and bootstrap confidence interval for R are also presented. Bayes estimate and credible interval are studied using Gibbs sampling technique. Monte Carlo simulations are performed to compare the performance of different proposed estimation methods. Analysis of a real data set is presented for illustrative purposes.
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