Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Kullback-Leibler Information of Consecutive Order Statistics

  • Kim, Ilmun (Department of Statistics, Carnegie Mellon University) ;
  • Park, Sangun (Department of Applied Statistics, Yonsei University)
  • Received : 2015.07.17
  • Accepted : 2015.08.20
  • Published : 2015.09.30
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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.

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References

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