A NEW GENERALIZED VARENTROPY AND ITS PROPERTIES

• Main Authors: Saeid Maadani, Gholam Reza Mohtashami Borzadaran, Abdol Hamid Rezaei Roknabadi
• Format: Article
• Language: English
• Published: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. 2020-07-01
• Series: Ural Mathematical Journal
• Subjects: generalized varentropy, past tsallis varentropy, residual tsallis varentropy, tsallis varentropy, varentropy.
• Online Access: https://umjuran.ru/index.php/umj/article/view/197

The variance of Shannon information related to the random variable \(X\), which is called varentropy, is a measurement that indicates, how the information content of \(X\) is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them.