Related papers: Relative variation indexes for multivariate contin…
This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness,…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect the CV. Additionally, for skewed distributions the mean…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk…
The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…
The coefficient of variation, which measures the variability of a distribution from its mean, is not uniquely defined in the multidimensional case, and so is the multidimensional Gini index, which measures the inequality of a distribution…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
Given a variety over $\mathbb{Q}$, we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise…
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…
The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian…
We evaluate the dependence among the margins of a random vector with Multivariate Extreme Value distribution throughout the expected value of a range and relate this coefficient of dependence with the multivariate tail dependence. Its…
A new family of multivariate distributions, which shall be termed multivector variate distributions, based in the family of the multivariate contoured elliptically distribution is proposed. Several particular cases of multivector variate…
This paper proposes new estimators for the propensity score that aim to maximize the covariate distribution balance among different treatment groups. Heuristically, our proposed procedure attempts to estimate a propensity score model by…
Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
This article proposes the application of various alternative definitions of the multivariate coefficient of variation parameter in two domains: radar polarimetric time series and dynamic polarimetric speckle. In the first case, the focus is…