Some properties of cumulative Tsallis entropy of order $$\alpha $$ α

Abstract

Tsallis entropy of order \(\alpha \) (see Tsallis in J Stat Phys 52(1–2):479–487, 1988) plays an important role in the measurement uncertainty of random variables. Recently, Sati and Gupta (J Probab Stat, doi:10.1155/2015/694203, 2015) introduced a cumulative Tsallis entropy of order \(\alpha \) and studied its various properties in the context of reliability modeling. In this paper, we introduce an alternate measure of cumulative Tsallis entropy of order \(\alpha \) and study its properties. Unlike the cumulative Tsallis entropy due to Sati and Gupta (J Probab Stat, doi:10.1155/2015/694203, 2015), the proposed measure has some additional features and has simple relationships with other important information and reliability measures.