Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew-normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew-normal factor are equivalent to those under a quadratic model up to third-order moments. The reverse only ho...

This paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. Firit, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a sing...

This paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. First, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a sing...

In this paper, we assume the error distribution of one-way ANOVA as alpha-skew normal distribution. Alpha-skew gives us exibility for modelling data which has heavy tailness, skewness, bimodality and also symmetricity. We obtain maximum likelihood estimator model parameters test statistics based on these estimators. Monte Carlo simulation study states that estimators interest are more efficient...

Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs.

PURPOSE Skew deviation is a vertical strabismus caused by damage to the otolithic-ocular reflex pathway and is associated with abnormal ocular torsion. This study was conducted to determine whether patients with skew deviation show the normal pattern of three-dimensional eye control called Listing's law, which specifies the eye's torsional angle as a function of its horizontal and vertical posi...

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...

Hallin and Ley (2012) investigate and fully characterize the Fisher singularity phenomenon in univariate and multivariate families of skew-symmetric distributions. This paper proposes a refined analysis of the (univariate) Fisher degeneracy problem, showing that it can be more or less severe, inducing n (“simple singularity”), n (“double singularity”), or n (“triple singularity”) consistency ra...

Finite mixtures of skew distributions provide a flexible tool for modelling heterogeneous data with asymmetric distributional features. However, parameter estimation via the Expectation-Maximization (EM) algorithm can become very timeconsuming due to the complicated expressions involved in the E-step that are numerically expensive to evaluate. A more time-efficient implementation of the EM algo...

Let {Xn, n ≥ 1} be independent and identically distributed random variables with each Xn following skew normal distribution. Let Mn = max{Xk, 1 ≤ k ≤ n} denote the partial maximum of {Xn, n ≥ 1}. Liao et al. (2014) considered the convergence rate of the distribution of the maxima for random variables obeying the skew normal distribution under linear normalization. In this paper, we obtain the a...