On cumulative residual entropy of progressively censored order statistics

2018 ◽  
Vol 139 ◽  
pp. 47-52
Author(s):  
Z.A. Abo-Eleneen ◽  
B. Almohaimeed ◽  
H.K.T. Ng
Keyword(s):  
Order Statistics ◽  
Residual Entropy ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual

On Cumulative Residual Renyi Entropy of Consecutive Order Statistics

2017 ◽  
Vol 14 (1) ◽  
pp. 615-619
Author(s):  
Z. A Abo-Eleneen ◽  
Bader Almohaimeed
Keyword(s):  
Order Statistics ◽  
Recurrence Relations ◽  
Simple Expression ◽  
Computational Method ◽  
Residual Entropy ◽  
Cumulative Residual Entropy ◽  
Renyi’S Entropy ◽  
Single Integral ◽  
Cumulative Residual ◽  
Sample Estimate

Rao et al. (2004, IEEE Transactions on Information Theory, 50, 1220–1228). proposed cumulative residual entropy (CRE): a new and robust measure of information. Recently Sunoj and Linu (2012, Statistics, 46:1, 41–56,) discussed the cumulative residual Renyi’s entropy CRREα as a generalized of CRE. In this paper, we first provide a computational method that represents the joint CRREα of the first i order statistics as a single integral and it further, simplifying to simple expression as sum of the beta distributions. We then derive some recurrence relations for the CRREα in a consecutive order statistics to facilitate the computation. We also develop a simple formula for the sample estimate of the CRREα of a consecutive order statistics.

Generalized Cumulative Residual Entropy of Time Series Based on Permutation Patterns

2021 ◽  
pp. 2150055
Author(s):  
Qin Zhou ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Stock Markets ◽  
Multiple Scales ◽  
Permutation Entropy ◽  
Residual Entropy ◽  
Permutation Patterns ◽  
Cumulative Residual Entropy ◽  
The Us ◽  
Cumulative Residual ◽  
Different Characteristics

Cumulative residual entropy (CRE) has been suggested as a new measure to quantify uncertainty of nonlinear time series signals. Combined with permutation entropy and Rényi entropy, we introduce a generalized measure of CRE at multiple scales, namely generalized cumulative residual entropy (GCRE), and further propose a modification of GCRE procedure by the weighting scheme — weighted generalized cumulative residual entropy (WGCRE). The GCRE and WGCRE methods are performed on the synthetic series to study properties of parameters and verify the validity of measuring complexity of the series. After that, the GCRE and WGCRE methods are applied to the US, European and Chinese stock markets. Through data analysis and statistics comparison, the proposed methods can effectively distinguish stock markets with different characteristics.

scholarly journals Generalized Entropies, Variance and Applications

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 709 ◽  
Author(s):  
Abdolsaeed Toomaj ◽  
Antonio Di Crescenzo
Keyword(s):  
Residual Entropy ◽  
Dispersion Measure ◽  
Homogeneous Poisson Process ◽  
Cumulative Residual Entropy ◽  
Excess Wealth Order ◽  
Dynamic Version ◽  
Cumulative Residual ◽  
Non Homogeneous Poisson Process ◽  
Generalized Entropies ◽  
Cumulative Entropy

The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order. We also obtain similar results for the generalized cumulative entropy, which is a dual measure to the generalized cumulative residual entropy.

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