On estimation of weighted cumulative residual Tsallis entropy for complete and censored samples

Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure. Next, we propose some non-parametric estimators of this measure. Asymptotic properties of these estimators are discussed. Performance of these estimators are compared by mean squared error. Non-parametric estimators for weighted cumulative residual entropy measure are also discussed. Estimator for weighted cumulative residual Tsallis entropy for progressive type-II censored data is proposed and its performance is investigated by Monte-Carlo simulations for various censoring schemes. Two uniformity tests for complete samples are proposed based on an estimator of these two measures and power of the tests are compared with some popular tests. The tests perform reasonably well. Uniformity test under progressively type-II censored data is also developed. Some real datasets are analysed for illustration.

💡 Research Summary

The paper introduces and studies the weighted cumulative residual Tsallis entropy (WCRTE), a generalization of the weighted cumulative residual entropy (WCRE) that incorporates a Tsallis‑type parameter α. After reviewing Shannon entropy, Tsallis entropy, and cumulative residual entropy (CRE), the authors define the weighted version for a non‑negative continuous random variable X as

\