On estimation of Tsallis entropy for exponentially distributed doubly type-II censored sample

Tsallis entropy, as a generalized measure of uncertainty, plays a vital role in characterizing complex systems exhibiting long-range dependence and non-extensive behaviour. We discuss the problem of affine equivariant estimation of Tsallis entropy for a two-parameter exponentially distributed doubly Type-II censored sample. The minimum risk equivariant estimator (MREE) is derived for the parametric function associated with the Tsallis entropy under a general bowl-shaped scale-equivariant loss function. Its inadmissibility is shown by constructing improved estimators using Stein’s framework. Further, a smooth Brewster–Zidek type estimator is derived, which consistently dominates the MREE in terms of risk and offers improved numerical stability under varying degrees of censoring. Sufficient conditions are derived through Kubokawa’s integral expressions to show the risk reduction of the proposed estimators. The simulation study shows that the proposed improved estimators exhibit greater improvement under the entropy loss function than under the quadratic loss function. Furthermore, the scale-equivariant property of the improved estimators enables the estimation of Tsallis entropy across different scales, and a notable reduction in Tsallis entropy is observed for real-life phenomena, as illustrated using six different datasets.