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 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 order statistics according to r and discuss its relation with Fisher information in order statistics.
Bibliographical noteFunding Information:
The author is grateful to anonymous referees and an associate editor for making some useful comments on an earlier version of this manuscript. This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2011-0029104) and the Korea government (MEST) (No. 2012-004905).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty