Generalized measures of information for truncated random variables

<Para ID="Par1">In the present work we focus on the generalization of two types of measures of information namely divergence-type and entropy-type. Kullback–Leibler discrimination measure and Shannon entropy have been considered in this context for truncated random variables. We propose a generalized discrimination measure between two residual and past lifetime distributions along a similar line of Varma’s entropy. Some properties of this measure are studied and a characterization of the proportional (reversed) hazards model is given. Furthermore, Shannon entropy is generalized on the basis of Varma’s entropy for past lifetime distribution. These results generalize and enhance the related existing results that are developed based on Kullback–Leibler information and Shannon entropy. Copyright Springer-Verlag Berlin Heidelberg 2015