• Modeling real data sets, even when we have some potential (as)symmetric models for the underlying data distribution, is always a very difficult task due to some uncontrollable perturbation factors. The analysis of different data sets from diverse areas of application, and in particular from statistical process control (SPC), leads us to notice that they usually exhibit moderate to strong asym...

In this work we approach the problem of model comparison between skew families. For the univariate skew model, we measure the sensitivity of the skewness parameter using the L1-distance between symmetric and asymmetric models and we obtain explicit expressions for some of these models. The main result is that the L1-distance between a representable elliptical distribution and a representable sk...

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...

We discuss tail behaviors, subexponentiality and extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. It shows that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distr...

Skew orthogonal polynomials arise in the calculation of the n-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials. In the cases that the eigenvalue probability density function involves a classical weig...

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a num...

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 ...