To model multivariate, possibly heavy-tailed data, we compare the multivariate normal model (N) with two versions of the multivariate Student model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). After recal...
A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) geometric stable distributions are extended to a more general case of “anisotropic” random summation where sums...
Multivariable time series prediction has been widely studied in power energy, aerology, meteorology, finance, transportation, etc. Traditional modeling methods have complex patterns and are inefficient to capture long-term multivariate dependencies o...
Maps are one of the most conventional types of visualization used when conveying information to both inexperienced users and advanced analysts. However, the multivariate representation of data on maps is still considered an unsolved problem. We prese...
The aim of this paper is to construct two new classes of multivariate risk statistics, and to study their properties. We, first, introduce the multivariate shortfall risk statistics and multivariate divergence risk statistics. Then, their basic prope...
Multivariate count data are often modeled via a multivariate Poisson distribution, but it contains an underlying, constraining assumption of data equi-dispersion (where its variance equals its mean). Real data are oftentimes over-dispersed and, as su...
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced. Some properties of these...
In this paper, I consider multivariate analogues of the extended gamma density, which will provide multivariate extensions to Tsallis statistics and superstatistics. By making use of the pathway parameter
This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, for the moments and cumulants of spherically and elliptically symmetric multivariate distributions; results for the case of multivariate t-di...
The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and ins...
The modified Dagum distribution is a highly versatile statistical model, and it is included in several important parametric families of distributions, with applications, such as economics and public health. In this paper, we introduce a multivariate...
Many important exposure–response relationships, such as diet and weight, can be influenced by intermediates, such as the gut microbiome. Understanding the role of these intermediates, the mediators, is important in refining cause–effect t...
Multiscale entropy (MSE) was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i) a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii) the computation of the...
The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-bas...
Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular no...
Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relatio...
Multivariate tail coefficients are an important tool when investigating dependencies between extreme events for different components of a random vector. Although bivariate tail coefficients are well-studied, this is, to a lesser extent, the case for...
This paper introduces a multivariate extension of Raftery copula. The proposed copula is exchangeable and expressed in terms of order statistics. Several properties of this copula are established. In particular, the multivariate Kendall’s tau a...
Multivariate quantiles are of increasing importance in applications of hydrology. This calls for reliable methods to evaluate the precision of the estimated quantile sets. Therefore, we focus on two recently developed approaches to estimate confidenc...
In order to improve the accuracy of wind power prediction (WPP), we propose a WPP based on multivariate phase space reconstruction (MPSR) and multivariate linear regression (MLR). Firstly, the multivariate time series (TS) are constructed through rea...
Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While th...
Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matr...
Accurate multivariate Gaussian simulation is critical for resource assessment and mine planning, especially in polymetallic deposits where strong trends, data bias, and multivariate outliers introduce complexity. In this scenario, standard workflows...
The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate i...
Moran’s I is a spatial autocorrelation measure of univariate spatial data. Therefore, even if p spatial data exist, we can only obtain p values for Moran’s I. In other words, Moran’s I cannot measure the degree of spatial autocorrel...
In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the ord...
A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that in...
The multivariate skew-normal distribution is useful for modeling departures from normality in data through parameters controlling skewness. Recently, several extensions of this distribution have been proposed in the statistical literature, among whic...
Multivariate normal moments are foundational for statistical methods. The derivation and simplification of these moments are critical for the accuracy of various statistical estimates and analyses. Normal moments are the building blocks of the Hermit...
In this article, we employ the uniform and
The multivariate normal is a common assumption in many statistical models and methodologies for high-dimensional data analysis. The exploration of approaches to testing multivariate normality never stops. Due to the characteristics of the multivariat...
The multivariate skew-t distribution plays an important role in statistics since it combines skewness with heavy tails, a very common feature in real-world data. A generalization of this distribution is the truncated multivariate skew-t distribution...
While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a...
We introduce a quantile-based multivariate log-normal distribution, providing a new multivariate skewed distribution with positive support. The parameters of this distribution are interpretable in terms of quantiles of marginal distributions and asso...
Wind turbine planetary gearboxes have complex structures and operating environments, which makes it difficult to extract fault features effectively. In addition, it is difficult to achieve efficient fault diagnosis. To improve the efficiency of featu...
The efficiency of sampling is a critical concern in Monte Carlo analysis, which is frequently used to assess the effect of the uncertainty of the input variables on the uncertainty of the model outputs. The projection pursuit multivariate transform i...
Many existing natural scene statistics-based no reference image quality assessment (NR IQA) algorithms employ univariate parametric distributions to capture the statistical inconsistencies of bandpass distorted image coefficients. Here, we propose a...
We consider here multivariate data which we understand as the problem where each data point i is measured for two or more distinct variables. In a typical situation there are many data points i while the range of the different variables is more limit...
The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit...
The complex data characteristics collected in Industry 4.0 cannot be efficiently handled by classical Six Sigma statistical toolkit based mainly in least squares techniques. This may refrain people from using Six Sigma in these contexts. The incorpor...
Multivariate Statistical Process Control (MSPC) seeks to monitor several quality characteristics simultaneously. However, it has limitations derived from its inability to identify the source of special variation in the process. In this research, a pr...
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defin...
In this article, a multivariate extension of the unit-sinh-normal (USHN) distribution is presented. The new distribution, which is obtained from the conditionally specified distributions methodology, is absolutely continuous, and its marginal distrib...
I give for the first time explicit formulas for the coefficients needed for the fourth-order Edgeworth expansions of a multivariate standard estimate. I call these the Edgeworth coefficients. They are Bell polynomials in the cumulant coefficients. St...
We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows the conditional variance of log-returns of each bank...
With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large...
Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula a...
In this article we give sufficient conditions for stochastic order of multivariate uniform distributions on closed convex sets.
Widespread deployment of spectrally efficient mobile networks, advancements in mobile devices, and proliferation of attractive applications has led to an exponential increase in mobile data traffic. Mobile Network Operators (MNOs) benefit from the as...
The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components, we can...
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