Some Reliability Properties of Bivariate Cumulative Residual Tsallis Entropy

• Published in: Journal of statistical theory and practice Vol. 14; no. 4
• Main Authors: Raju, David Chris, Sunoj, S. M., Rajesh, G
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2020
• Subjects: Mathematics and Statistics; Original Article; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; Tsalli’s entropy; Bivariate models; Cumulative residual entropy; Empirical survival function; 94A17; 62N05; Reliability measures
• ISSN: 1559-8608; 1559-8616
• DOI: 10.1007/s42519-020-00129-0

Rajesh and Sunoj (Stat Pap 60(3):583–593, 2019) have introduced an alternative form of cumulative Tsalli’s Entropy for continuous random variables and studied its importance in reliability studies. The present study aims at extending this measure to the bivariate case based on two types of conditioning, viz. conditionally specified and survival models. In a two component system, it measures the uncertainty associated with one component when the other component is either failed or survived a specified period of time. Characterization results are established for important bivariate lifetime models. We also propose an empirical and kernel-based plug-in estimators for conditional cumulative Tsalli’s entropy and study its performance using simulated data. A real data analysis is also carried out to evaluate the usefullness of the empirical estimator of a bivariate dynamic cumulative Tsalllis entropy and compared its performance with that of similar estimator due to Sati and Singh (J Appl Math Inf 35(1–2):45–58, 2017).