Cumulative residual entropy: a new measure of information

By Murali Rao, Yunmei Chen, Baba C. Vemuri, Fei Wang. IEEE Transactions on Information Theory, 2004

607 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/70f3ca595b2d32a90fea3f426467625df6453c76

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Citations in the corpus

Characterizations Based on Cumulative Residual Entropy of First-Order Statistics (2010, background): “( 2004 ) introduced a new measure of information that extends the Shannon entropy to continuous random variables, and called it cumulative residual entropy (CRE).”
Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data (2019, neutral): “Finally, consider the cumulative residual entropy (Rao et al. 2004)defined by =c = ∫ Pr(X > x)logPr(X > x)dx. (23) Using the series expansions, (1− x)n−1 = ∞∑ p=0 (−1)p ( n− 1 p ) xp (24) and log(1− x) = − ∞∑ p=1 xp p , one calculate (23) as =c = ∞∑ i=1 1 i ∫ ∞ 0 [ α[1− 1+θ+θx 1+θ ]e −θx − 1 α− 1…”
On negative cumulative extropy with applications (2020, methodology): “If we assume that EðCJ ðXjFÞÞ ¼ 0, then CJ ðXjFÞ ¼ 0: Recalling the definition of CJ ðXjFÞ, we immediately conclude that EðIðX xÞjFÞ ¼ 1: Thanks to the use of relation (24) of Rao et al. (2004), X is F -measurable.”
A new discrete distribution (2014, background): “The cumulative residual entropy [50] is defined by”
Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy (2015, background): “( For a residual lifetime 𝑋 𝑡 = [𝑋 − 𝑡 | 𝑋 > 𝑡] , where 𝑡 > 0 , Ebrahimi [2] defined an entropy as a dynamic measure of uncertainty which is given by Alternative entropy was introduced by Rao et al. [3] which is based on survival function instead of probability density function.”
On weighted cumulative residual entropy (2017, methodology): “ForWCRE, we prove following theorem, which is analogous to Proposition 2 of Rao et al. (2004).”
ON CUMULATIVE RESIDUAL EXTROPY (2020, background): “[20] have shown that ξ(X) ≤ (E(X(2)))/(2E(X)).”
On weighted extropies (2020, background): “0 xyf (2)(x, y)dxdy, (16) where X and Y are non-negative random variables with joint density function f(x, y).”