In recent years, the skew-normal models introduced by Azzalini (1985)—and their multivariate generalizations from Azzalini and Dalla Valle (1996)—have enjoyed an amazing success, although an important literature has reported that they exhibit, in the vicinity of symmetry, singular Fisher information matrices and stationary points in the profile log-likelihood function for skewness, with the usu...

Non-normal mixture distributions have received increasing attention in recent years. Finite mixtures of multivariate skew-symmetric distributions, in particular, the skew normal and skew t-mixture models, are emerging as promising extensions to the traditional normal and t-mixture models. Most of these parametric families of skew distributions are closely related, and can be classified into fou...

Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model (LMM) framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the data set particularly exhibits skewness and heavy tails. Using a Bayesian paradigm...

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

In this article, we introduce the multivariate slash and skew-slash t distributions which provide alternative choices in simulating and fitting skewed and heavy tailed data. We study their relationships with other distributions and give the densities, stochastic representations, moments, marginal distributions, distributions of linear combinations and characteristic functions of the random vect...

In this paper, a multivariate fundamental skew probit (MFSP) model is used to model correlated ordinal responses which are constructed from the multivariate fundamental skew normal (MFSN) distribution originate to the greater flexibility of MFSN. To achieve an appropriate VC structure for reaching reliable statistical inferences, many types of variance covariance (VC) structures are considered ...

Sums of lognormal random variables (RVs) occur in many important problems in wireless communications especially in interferences calculation. Several methods have been proposed to approximate the lognormal sum distribution. Most of them requires lengthy Monte Carlo simulations, or advanced slowly converging numerical integrations for curve fitting and parameters estimation. Recently, it has bee...

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian (PS) splitting, and then establish a class of positivedefinite and skew-Hermitian splitting (PSS) methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS...