Extropy based inaccuracy measure in order statistics

Abstract

AbstractIn this paper, we provide a measure based on inaccuracy between distributions of the ith order statistic and the parent random variable. This measure characterizes the distribution function of parent random variable uniquely. We demonstrate that the extropy of the parent random variable is the average of the accuracy measure. It is also shown that the measure of inaccuracy defined is invariant under scale but not under location transformation. Nonparametric estimators for the proposed measures are also obtained. A Monte Carlo simulation study is performed to verify the performance of the suggested estimators. Simulation results show that the estimator based on the reflection boundary technique for probability density function estimation and the empirical method for cumulative distribution function estimation has the best performance among estimators. Also, a real dataset is considered to show an application of the proposed estimators on model selection.Keywords: Extropyinaccuracy measureorder statisticsnonparametric estimation2000 AMS Subject Classifications: Primary 62F10Secondary 62N05 AcknowledgmentsThe authors would like to thank two anonymous referees and the associate editor for their useful comments and constructive criticisms on the original version of this manuscript which led to this considerably improved version.Disclosure statementNo potential conflict of interest was reported by the author(s).