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http://dx.doi.org/10.5351/CSAM.2015.22.5.487

Kullback-Leibler Information of Consecutive Order Statistics  

Kim, Ilmun (Department of Statistics, Carnegie Mellon University)
Park, Sangun (Department of Applied Statistics, Yonsei University)
Publication Information
Communications for Statistical Applications and Methods / v.22, no.5, 2015 , pp. 487-494 More about this Journal
Abstract
A calculation of the Kullback-Leibler information of consecutive order statistics is complicated because it depends on a multi-dimensional integral. Park (2014) discussed a representation of the Kullback-Leibler information of the first r order statistics in terms of the hazard function and simplified the r-fold integral to a single integral. In this paper, we first express the Kullback-Leibler information in terms of the reversed hazard function. Then we establish a generalized result of Park (2014) to an arbitrary consecutive order statistics. We derive a single integral form of the Kullback-Leibler information of an arbitrary block of order statistics; in addition, its relation to the Fisher information of order statistics is discussed with numerical examples provided.
Keywords
cross entropy; entropy; Fisher information; Kullback-Leibler information; left-censoring; order statistics; reversed hazard function;
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