A new estimator of entropy and its application in testing normality

Noughabi, Hadi Alizadeh

doi:10.1080/00949650903005656

Cited by 67 publications

(8 citation statements)

References 13 publications

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“…Now the entropy is a characteristic playing a fundamental role not only in information theory and communication, but also in classification, pattern recognition, statistical physics, stochastic dynamics, statistics, etc. Just in statistics Shannon's entropy is used as a descriptive parameter (measure of dispersion), for testing normality (Vasicek in [15], Arizono and Ohta in [1], Noughabi in [10]), exponentiality (Grzegorzewski and Wieczorkowski in [6], Taufer in [13]) and uniformity (Dudewicz, et al in [4]), etc. (see also [3], [8], [11], [16], [17]).…”

Section: Entropymentioning

confidence: 99%

Statistical Tests for Comparing Pareto Charts

Grzegorzewski¹

2012

Communications in Numerical Analysis

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Section: Entropymentioning

confidence: 99%

Statistical Tests for Comparing Pareto Charts

Grzegorzewski¹

2012

Communications in Numerical Analysis

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“…2 of 21 methods have been discussed as a non-parametric approach in Refs. [13,14]. This strategy is flexible and robust because it does not enforce a model or parametric constraints.…”

Section: Introductionmentioning

confidence: 99%

Identifying Heterogeneity in SAR Data with New Test Statistics

Frery,

Alpala,

Nascimento

2024

Preprint

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This paper presents a statistical approach to identify the underlying roughness characteristics in synthetic aperture radar (SAR) intensity data. The physical modeling of this kind of data allows the use of the Gamma distribution in the presence of fully-developed speckle, i.e., when there are infinitely many independent backscatterers per resolution cell, and none dominates the return. Such areas are often called ``homogeneous'' or ``textureless'' regions. The GI0 distribution is also a widely accepted law for heterogeneous and extremely heterogeneous regions, i.e., areas where the fully-developed speckle hypotheses do not hold. We propose three test statistics to distinguish between homogeneous and inhomogeneous regions, i.e., between gamma and GI0 distributed data, both with a known number of looks. The first test statistic uses a bootstrapped non-parametric estimator of Shannon entropy, providing a robust assessment in uncertain distributional assumptions. The second test uses the classical coefficient of variation (CV). The third test uses an alternative form of estimating the CV based on the ratio of the mean absolute deviation from the median to the median. We apply our test statistic to create maps of \(p\)-values for the homogeneity hypothesis. Finally, we show that our proposal, the entropy-based test, outperforms existing methods, such as the classical CV and its alternative variant, in identifying heterogeneity when applied to both simulated and actual data.

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“…Shannon entropy is a crucial descriptive parameter in statistics, especially for evaluating data dispersion and performing tests for normality, exponentiality and uniformity [11,12]. Entropy estimation is challenging, especially when the model is unknown; in these cases, non-parametric methods, as those based on spacings [13,14], can be used. This strategy is flexible and robust because it does not enforce a model or parametric constraints.…”

Section: Introductionmentioning

confidence: 99%

Identifying Heterogeneity in SAR Data with New Test Statistics

Frery,

Alpala,

Nascimento

2024

Remote Sensing

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This paper presents a statistical approach to identify the underlying roughness characteristics in synthetic aperture radar (SAR) intensity data. The physical modeling of this kind of data allows the use of the Gamma distribution in the presence of fully developed speckle, i.e., when there are infinitely many independent backscatterers per resolution cell, and none dominates the return. Such areas are often called “homogeneous” or “textureless” regions. The GI0 distribution is also a widely accepted law for heterogeneous and extremely heterogeneous regions, i.e., areas where the fully developed speckle hypotheses do not hold. We propose three test statistics to distinguish between homogeneous and inhomogeneous regions, i.e., between gamma and GI0 distributed data, both with a known number of looks. The first test statistic uses a bootstrapped non-parametric estimator of Shannon entropy, providing a robust assessment in uncertain distributional assumptions. The second test uses the classical coefficient of variation (CV). The third test uses an alternative form of estimating the CV based on the ratio of the mean absolute deviation from the median to the median. We apply our test statistic to create maps of p-values for the homogeneity hypothesis. Finally, we show that our proposal, the entropy-based test, outperforms existing methods, such as the classical CV and its alternative variant, in identifying heterogeneity when applied to both simulated and actual data.

show abstract

A new estimator of entropy and its application in testing normality

Cited by 67 publications

References 13 publications

Statistical Tests for Comparing Pareto Charts

Statistical Tests for Comparing Pareto Charts

Identifying Heterogeneity in SAR Data with New Test Statistics

Identifying Heterogeneity in SAR Data with New Test Statistics

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