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Inferences Using Lower Record Values of Inverted Exponentiated Pareto Distribution
Abstract
This article presents the classical and Bayesian inferences for the inverted exponentiated Pareto (IEP) distribution assuming lower record values. We first derive the expression for r-th row moment of m-th lower record and then use these results to compute the means, variances , skewnesses and kurtosises for the lower records. Next we consider maximum likelihood and Bayes estimations of the parameters of the IEP distribution. Under these approaches asymptotic confidence intervals and Bayes credible interval estimates of the parameters are also obtained. The Bayes estimation is studied under squared error loss function as well as LINEX loss function. Finally, we compute predictive estimates and predictive interval estimates for the future lower record values using classical and Bayesian approaches. We have used an importance sampling method in Bayesian setup. Moreover, a comparison between classical and Bayesian approaches is also done using simulations. Besides the simulation study, a real data set is considered to show the application of the study.
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