scholarly journals Overlap invariance of cumulative residual entropy measures for multimodal image alignment

2009 ◽  
Author(s):  
Nathan D. Cahill ◽  
Julia A. Schnabel ◽  
J. Alison Noble ◽  
David J. Hawkes
Keyword(s):  
Image Alignment ◽  
Residual Entropy ◽  
Entropy Measures ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual

scholarly journals Fractional Entropy-Based Test of Uniformity with Power Comparisons

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed S. Mohamed ◽  
Haroon M. Barakat ◽  
Salem A. Alyami ◽  
Mohamed A. Abd Elgawad
Keyword(s):  
Simulation Study ◽  
Limit Distribution ◽  
Residual Entropy ◽  
Test Statistic ◽  
Percentage Points ◽  
Entropy Measures ◽  
Cumulative Residual Entropy ◽  
Power Comparisons ◽  
Fractional Entropy ◽  
Cumulative Residual

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

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.

Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty

2020 ◽  
Vol 19 (04) ◽  
pp. 2050038
Author(s):  
Keqiang Dong ◽  
Xiaofang Zhang
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Higher Order ◽  
Stationary Time Series ◽  
Residual Entropy ◽  
Third Order ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual ◽  
Simulated Time ◽  
Analyze Time Series

The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated time series generated by uniform distribution on [0, 1]. Finally, we present the application of higher-order multiscale fractional cumulative residual entropy in logistic map time series and stock markets time series, respectively.

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