Some results on Tsallis entropy measure and k-record values

Extensive or non-extensive statistical mechanics arise from the additive or non-additivity of the corresponding entropy measures. Non-additive entropy measures are important for many applications. In this article, we consider and study a non-additive Tsallis entropy for k-record statistics from some continuous probability models. Furthermore, we prove a characterization result for the Tsallis entropy of k-record values. At the end, we study Tsallis residual entropy for k-record statistics.