On weighted cumulative Tsallis residual and past entropy measures

In this work, we propose weighted cumulative Tsallis residual and past entropy measures and their dynamic versions. The properties of the proposed entropy measures are studied. It is shown that the residual entropy uniquely determines the survival function. Characterizations for Rayleigh and Power distributions are obtained based on the proposed entropy measures. The empirical versions of the residual and past entropies are provided and their asymptotic behaviors are discussed. It is shown that the weighted cumulative Tsallis entropy can be used as a risk measure. A dataset is analyzed for illustrative purposes.