- Mathematics; Physics and Astronomy
In the present paper, we propose a quantile version of Tsallis- α divergence and study its various properties. Examples are given in support of the importance of proposed quantile-based approach over traditional distribution-based approach. We consider quantile-based Tsallis- α divergence when random variables are truncated from both ends. Properties including bounds and inequalities are studied. Characterizations are obtained. The effects of transformations are discussed. Further, as a special case of the quantile-based doubly truncated Tsallis- α divergence, we provide a brief discussion on quantile-based residual and past Tsallis- α divergence.