On Cumulative Residual Renyi Entropy of Consecutive Order Statistics

Abstract

Rao et al. (2004, IEEE Transactions on Information Theory, 50, 1220–1228). proposed cumulative residual entropy (CRE): a new and robust measure of information. Recently Sunoj and Linu (2012, Statistics, 46:1, 41–56,) discussed the cumulative residual Renyi’s entropy CRREα as a generalized of CRE. In this paper, we first provide a computational method that represents the joint CRREα of the first i order statistics as a single integral and it further, simplifying to simple expression as sum of the beta distributions. We then derive some recurrence relations for the CRREα in a consecutive order statistics to facilitate the computation. We also develop a simple formula for the sample estimate of the CRREα of a consecutive order statistics.