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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 G I 0 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 G I 0 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. [ABSTRACT FROM AUTHOR]

We propose a new autoregressive moving average (ARMA) process with generalized gamma (GΓ$$ \Gamma $$) marginal law, called GΓ$$ \Gamma $$‐ARMA. We derive some of its mathematical properties: moment‐based closed‐form expressions, score function, and Fisher information matrix. We provide a procedure for obtaining maximum likelihood estimates for the GΓ$$ \Gamma $$‐ARMA parameters. Its performance is quantified and discussed using Monte Carlo experiments, considering (among others) various link functions. Finally, our proposal is applied to solve remote sensing problems using synthetic aperture radar (SAR) imagery. In particular, the GΓ$$ \Gamma $$‐ARMA process is applied to real data from images taken in the Munich and San Francisco regions. The results show that GΓ$$ \Gamma $$‐ARMA describes the neighborhoods of SAR features better than the gamma‐ARMA process (a reference for asymmetric positive data). For pixel ray modeling, our proposal outperforms 풢I0 and gamma‐ARMA. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar is an efficient remote sensing tool by producing high spacial resolution images. But, synthetic aperture radar data suffer speckle noise effect that difficult their processing (for example, making boundary detection). We propose and assess edge detectors for synthetic aperture radar imagery based on stochastic distances between models. These edge detectors stem from generalized divergences with good asymptotic properties. Results reveal that divergence-based detectors can outperform the likelihood-based counterpart. [ABSTRACT FROM AUTHOR]

Polarimetric Synthetic Aperture Radar (PolSAR) is one of the most important remote sensing tools. However, PolSAR images are strongly contaminated by a multidimensional interference (called speckle noise), making their processing (e.g. in the classification context) difficult. In terms of structure, multilook PolSAR data follow a definite positive hermitian behaviour and, therefore, require tailored classifiers for their features. Some classic classifiers – such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), K-Nearest Neighbours (KNN), and Support Vector Machine (SVM) – have been yielding unacceptable performance to these data, when applied directly. One justification is because they do not often take into account neither the speckle presence nor properties which are inherent to under-study relieves. This paper addresses a collection of PolSAR divergence-based classifiers, deduced from the normal, skew-normal, t-Student, and skew-t vector models as well as the scaled complex Wishart (SCW) distribution. The last model is a standard supposition to describe multilook PolSAR data, having two parameters: covariance matrix (which is directed to data nature) and number of looks (which controls the speckle noise effect). The considered remainder laws aim to model the main diagonal of these data, known as multivariate intensities. The performance of proposed methods is quantified and compared with those due to the Kullback-Leibler (KL) distance for multivariate normal distribution and to LDA, QDA, KNN, and SVM methods. Experiments with both artificial and real PolSAR data are considered. Results favour optimal Rényi classifiers for an Airborne Synthetic Aperture Radar (AIRSAR) image of San Francisco and the t-Student KL classifier for an SAR image system of the Electromagnetics Institute (EMISAR) image of Foulum. [ABSTRACT FROM AUTHOR]

Directional data are related to vectors on the unit sphere. When these vectors are not signed, this kind of data is called axial data. The Watson distribution is one of the main models for axial data. This model is equipped by two parameters: dominant axis and concentration. Based on the Rényi divergence and the Bhattacharya and Hellinger distances, we propose three hypothesis tests to check if two samples come from populations having the same concentration parameter. Results from synthetic and real data indicate that the proposed tests can yield good performance on Watson data. [ABSTRACT FROM AUTHOR]

We study a new family of continuous distributions with two extra shape parameters called the Burr generalized family of distributions. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for some of its mathematical quantities. The estimation of the model parameters is performed by maximum likelihood. We prove the flexibility of the new family by means of applications to two real data sets. Furthermore, we propose a new extended regression model based on the logarithm of the Burr generalized distribution. This model can be very useful to the analysis of real data and provide more realistic fits than other special regression models. [ABSTRACT FROM PUBLISHER]

The proposal of more exible distributions is an activity often required in practical contexts. In particular, adding a positive real parameter to a probability distribution by exponentiation of its cumulative distribution function has provided exible generated distributions having interesting statistical properties. In this paper, we study general mathematical properties of a new generator of continuous distributions with three extra parameters called the exponentiated Gompertz generated (EGG) family. We present some of its special models as well as an essay on its physical motivation. From mathematical point of view, we derive explicit expressions of the EGG family: the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics, which are valid for any baseline model. We also provide a bivariate EGG extension. The estimation procedure by maximum likelihood of the new class is elaborated and discussed. In order to quantify and to assess the asymptotic behavior of this procedure, we perform a simulation study. Finally, two applications to real data are performed. Results furnish evidence in favor of the use of the EGG beta distribution as a good proposal to these data sets. [ABSTRACT FROM AUTHOR]

This work presents a comprehensive examination of the use of information theory for understanding polarimetric synthetic aperture radar (PolSAR) images by means of contrast measures that can be used as test statistics. Due to the phenomenon called 'speckle', common to all images obtained with coherent illumination such as PolSAR imagery, accurate modelling is required in their processing and analysis. The scaled multilook complex Wishart distribution has proven to be a successful approach for modelling radar backscatter from forest and pasture areas. Classification, segmentation, and image analysis techniques, which depend on this model, have been devised, and many of them employ some kind of dissimilarity measure. Specifically, we introduce statistical tests for analyzing contrast in such images. These tests are based on the Bhattacharyya, chi-square, Hellinger, Kullback-Leibler and Rényi distances. Results obtained by Monte Carlo experiments reveal the Kullback-Leibler distance as the best one with respect to the empirical test sizes under several situations which include pure and contaminated data. The proposed methodology is applied to actual data, obtained by an E-SAR sensor over surroundings of Weßling, Bavaria, Germany. [ABSTRACT FROM AUTHOR]

Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser, and synthetic aperture radar, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G0 distribution and, under which, regions with different degrees of roughness and mean brightness can be characterized by two parameters; a third parameter, which is the number of looks, is related to the overall signal-to-noise ratio. Assessing distances between samples is an important step in image analysis; they provide grounds of the separability and, therefore, of the performance of classification procedures. This paper derives and compares eight stochastic distances and assesses the performance of hypothesis tests that employ them and maximum likelihood estimation. We conclude that tests based on the triangular distance have the closest empirical size to the theoretical one, while those based on the arithmetic--geometric distances have the best power. Since the power of tests based on the triangular distance is close to optimum, we conclude that the safest choice is using this distance for hypothesis testing, even when compared with classical distances as Kullback--Leibler and Bhattacharyya. [ABSTRACT FROM AUTHOR]

In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family. [ABSTRACT FROM AUTHOR]

The pandemic COVID-19 brings with it the need for studies and tools to help those in charge make decisions. Working with classical time series methods such as ARIMA and SARIMA has shown promising results in the first studies of COVID-19. We advance in this branch by proposing a risk factor map induced by the well-known Pearson diagram based on multivariate kurtosis and skewness measures to analyze the dynamics of deaths from COVID-19. In particular, we combine bootstrap for time series with SARIMA modeling in a new paradigm to construct a map on which one can analyze the dynamics of a set of time series. The proposed map allows a risk analysis of multiple countries in the four different periods of the pandemic COVID-19 in 55 countries. Our empirical evidence suggests a direct relationship between the multivariate skewness and kurtosis. We observe that the multivariate kurtosis increase leads to the rise of the multivariate skewness. Our findings reveal that the countries with high risk from the behavior of the number of deaths tend to have pronounced skewness and kurtosis values., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 Published by Elsevier Ltd.)

New generators are required to define wider distributions for modeling real data in survival analysis. To that end we introduce the four-parameter generalized beta-generated Lindley distribution. It has explicit expressions for the ordinary and incomplete moments, mean deviations, generating and quantile functions. We propose a maximum likelihood procedure to estimate the model parameters, which is assessed through a Monte Carlo simulation study. We also derive an additional estimation scheme by means of least square between percentiles. The usefulness of the proposed distribution to describe remission times of cancer patients is illustrated by means of an application to real data.