Kullback-Leibler Information of Consecutive Order Statistics | Zendy

Ilmun Kim | Zendy; Sangun Park | Zendy

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Kullback-Leibler Information of Consecutive Order Statistics

Author(s) -

Ilmun Kim,

Sangun Park

Publication year - 2015

Publication title -

communications for statistical applications and methods

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.326

H-Index - 6

eISSN - 2383-4757

pISSN - 2287-7843

DOI - 10.5351/csam.2015.22.5.487

Subject(s) - mathematics , kullback–leibler divergence , statistics , order statistic , function (biology) , fisher information , representation (politics) , evolutionary biology , politics , political science , law , biology

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.

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