In this paper, we first study doubly truncated (interval) Tsallis entropy and suggest doubly truncated (interval) cumulative residual Tsallis entropy (ICRT), which is an extension of cumulative residual Tsallis entropy (CRT) and the dynamic CRT defined by the aid of Sati and Gupta and of Kumar, re- spectively. We investigate some properties and characterization of this measure, such as its relation with doubly truncated Shannon entropy, mean residual (past) life, and hazard rate (or reversed hazard rate). Also, the twin measure, doubly truncated (interval) cumulative past Tsallis entropy, is determined, and some of its properties are studied. Moreover, their monotonicity and related aging classes of distributions are expressed, and the upper (lower) bound for them is acquired. In the end, we propose four nonpara- metric estimators and compare their performance by utilizing simulation data. Also, being based on the best-proposed estimator, a real data set is additionally examined.

Keywords