Abstract For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number properties are already known, but many others not, even some basic ones. The present contribution aims at filling missing gaps. Specifically, moments up to fourth order obtained, from here expressions Mardia’s measures skewness kurtosis. Other ...

Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in ...

Normality of random effects and error terms is a routine assumption for linear effects mixed models. However, such assumption may be unrealistic, obscuring important features of withinand among-unit variation. A simple and robust Bayesian parametric approach that relaxes this assumption by using a multivariate Skew elliptical distributions, which includes the Skew-t, Skew-normal, t-Student, and...

‎The goal of this study is to introduce an Asymmetric Uniform-Laplace (AUL) distribution‎. ‎We present a detailed theoretical description of this distribution‎. ‎We try to estimate the parameters of AUL distribution using the maximum likelihood method‎. ‎Since the likelihood approach results in complicated forms‎, ‎we suggest a bootstrap-based approach for es...