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

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.