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Maadani, S.; Borzadaran, G. Mohtashami; Roknabadi, A. Rezaei

A new generalized varentropy and its properties. (English) Zbl 1450.62006

Ural Math. J. 6, No. 1, 114-129 (2020).
Summary: 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.

MSC:

62B10 Statistical aspects of information-theoretic topics
94A17 Measures of information, entropy
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory

Keywords:

generalized varentropy; past Tsallis varentropy; residual Tsallis varentropy; Tsallis varentropy; varentropy
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\textit{S. Maadani} et al., Ural Math. J. 6, No. 1, 114--129 (2020; Zbl 1450.62006)
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