In recent years, the skew-normal models introduced in Azzalini (1985) 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 usual unpleasant consequences for inference. For general multivariate skew-symm...

Strand asymmetry in nucleotide composition is a remarkable feature of animal mitochondrial genomes. Understanding the mutation processes that shape strand asymmetry is essential for comprehensive knowledge of genome evolution, demographical population history and accurate phylogenetic inference. Previous studies found that the relative contributions of different substitution types to strand asy...

Given a conjugation C on separable complex Hilbert space H, bounded linear operator T H is said to be C-skew symmetric if CTC = -T*. This paper describes the maps, algebra of all operators acting that preserve difference for every H.

Canonical orders, introduced in the minimal model program for orders [CI05], are simultaneous generalisations of Kleinian singularities k[[s, t]], G < SL2 and their associated skew group rings k[[s, t]]∗G. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal res...

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study...

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.

In this paper, we analyze the returns of stocks comprising the German stock index DAX with respect to the α-stable distribution. We apply nonparametric estimation methods such as the Hill estimator as well as parametric estimation methods conditional on the α-stable distribution. We find for both the nonparametric and parametric estimation methods that the α-stable hypothesis cannot be rejected...

This work develops diagnostics for skew-t-normal nonlinear models which provides an useful extension for ordinary normal regression models when the data set under consideration involves heavy tail and asymmetric outcomes. The case-deletion model (CDM) is considered, and several diagnostic measures are derived and discussed. Furthermore, we discuss score test for homogeneity of the variance in s...

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field variational Bayes approximation of the posterior distribution to a skew-t likelihood and normal prior. Our simulations show that the proposed variational Bayes ap...