A quantile-based study of cumulative residual Tsallis entropy measures

In the present paper we introduce a quantile-based cumulative residual Tsallis entropy (CRTE) and quantile-based CRTE for order statistics. Unlike the cumulative residual Tsallis entropy measures in the distribution function approach due to Sati and Gupta (2015) and Rajesh and Sunoj (2016) respectively, the corresponding quantile versions possess some unique properties. In many applied works there do not have any tractable distribution functions while the quantile function exists and in such cases the proposed measures become more useful in measuring uncertainty of random variables. We obtain some characterizations for distributions based on the quantile versions of CRTE and derive certain bounds. We also study various properties of quantile-based CRTE for order statistics. (C) 2017 Elsevier B.V. All rights reserved.