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On Kullback–Leibler information of order statistics in terms of the relative risk

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  • Sangun Park

Abstract

The representation of the entropy in terms of the hazard function and its extensions have been studied by many authors including Teitler et al. (IEEE Trans Reliab 35:391–395, 1986 ). In this paper, we consider a representation of the Kullback–Leibler information of the first $$r$$ r order statistics in terms of the relative risk (Park and Shin in Statistics, 2012 ), the ratio of hazard functions, and extend it to the progressively Type II censored data. Then we study the change in Kullback–Leibler information of the first $$r$$ r order statistics according to $$r$$ r and discuss its relation with Fisher information in order statistics. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Sangun Park, 2014. "On Kullback–Leibler information of order statistics in terms of the relative risk," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 609-616, July.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:5:p:609-616
    DOI: 10.1007/s00184-013-0455-7
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    References listed on IDEAS

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    1. Sangun Park, 2003. "On the asymptotic Fisher information in order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 71-80, February.
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