Related papers: Sub-dimensional Mardia measures of multivariate sk…
This paper examines eight measures of skewness and Mardia measure of kurtosis for skew-elliptical distributions. Multivariate measures of skewness considered include Mardia, Malkovich-Afifi, Isogai, Song, Balakrishnan-Brito-Quiroz,…
For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present…
Kurtosis minus squared skewness is bounded from below by 1, but for unimodal distributions this parameter is bounded by 189/125. In some applications it is natural to compare distributions by comparing their kurtosis-minus-squared-skewness…
We consider the problem of testing multivariate normality when the data consists of a random sample of two-step monotone incomplete observations. We define for such data a generalization of Mardia's statistic for measuring kurtosis, derive…
Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
Extensive literature exists on how to test for normality, especially for identically and independently distributed (i.i.d) processes. The case of dependent samples has also been addressed, but only for scalar random processes. For this…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Skewness measures can be used to measure the level of asymmetry of a distribution. Given the prevalence of statistical methods that assume underlying symmetry, and also the desire for symmetry in order to make meaningful judgements for…
Multivariate scale mixtures of skew-normal (SMSN) variables are flexible models that account for non-normality in multivariate data scenarios by tail weight assessment and a shape vector representing the asymmetry of the model in a…
In a recent paper [\textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys. Rev. E 85, 066108 (2012)}], Cristelli \textit{et al.} analysed relation between skewness and kurtosis for complex dynamical systems and identified two power-law…
Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness $D_3$ is bounded from…
We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting…
We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance…
The unified skew-t (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
Skewness plays a relevant role in several multivariate statistical techniques. Sometimes it is used to recover data features, as in cluster analysis. In other circumstances, skewness impairs the performances of statistical methods, as in…
Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of $t$-distributions or an infinitely divisible family with finite variance. We prove…
Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…
The univariate Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this article, we define a skewed version of the Birnbaum-Saunders…