Some Results on a Generalized Residual Entropy based on Order Statistics

In the present paper, we discuss some monotone properties of the GRE of order (α, β) in order statistics under various assumptions. It is shown that monotone properties are preserved under the formation of a parallel system but not under the formation of a series system. A counter example is presented. Bounds of the GRE of order statistics are obtained. The GRE of parallel and series systems are shown to be monotone function of the number of observations of a given sample. Numerical simulation is carried out for verification of the theoretical results. Maximum likelihood estimators of GRE of X, X1:n and Xn:n are obtained when independent data are drawn from exponential distribution.

Abstract licence: CC BY

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