The Simultaneous Confidence Interval for the Ratios of the Coefficients of Variation of Multiple Inverse Gaussian Distributions and Its Application to PM2.5 Data

Chankham, Wasana; Niwitpong, Sa-Aat; Niwitpong, Suparat

doi:10.3390/sym16030331

Cited by 3 publications

(2 citation statements)

References 31 publications

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“…The coefficient of variation (CV), introduced in 1896 by Pearson [15], is a relative dispersion measure widely used in various fields of applied statistics, including sampling, biostatistics, medical and biological research, climatology and other fields [16][17][18][19]. It facilitates the comparison of variability between different populations and is particularly valuable for relating variables with different units.…”

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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Section: Introductionmentioning

confidence: 99%

Identifying Heterogeneity in SAR Data with New Test Statistics

Frery,

Alpala,

Nascimento

2024

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Identifying Heterogeneity in SAR Data with New Test Statistics

Frery,

Alpala,

Nascimento

2024

Remote Sensing

View full text Add to dashboard Cite

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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Estimating the Confidence Interval for the Common Coefficient of Variation for Multiple Inverse Gaussian Distributions

Chankham,

Niwitpong,

Niwitpong

2024

Symmetry

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The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving PM2.5 data from three provinces in northeastern Thailand that followed inverse Gaussian distributions.

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The Simultaneous Confidence Interval for the Ratios of the Coefficients of Variation of Multiple Inverse Gaussian Distributions and Its Application to PM2.5 Data

Cited by 3 publications

References 31 publications

Identifying Heterogeneity in SAR Data with New Test Statistics

Identifying Heterogeneity in SAR Data with New Test Statistics

Identifying Heterogeneity in SAR Data with New Test Statistics

Estimating the Confidence Interval for the Common Coefficient of Variation for Multiple Inverse Gaussian Distributions

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