Covariance Representations and Coherent Measures for Some Entropies

We obtain covariance and Choquet integral representations for some entropies and give upper bounds of those entropies. The coherent properties of those entropies are discussed. Furthermore, we propose tail-based cumulative residual Tsallis entropy of order α (TCRTE) and tail-based right-tail deviation (TRTD); then, we define a shortfall of cumulative residual Tsallis (CRTES) and shortfall of right-tail deviation entropy (RTDS) and provide some equivalent results. As illustrated examples, the CRTESs of elliptical, inverse Gaussian, gamma and beta distributions are simulated.