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...

 In this paper, we consider a flexible skew-generalized normal distribution. This distribution is denoted by $FSGN(/lambda _1, /lambda _2 /theta)$. It contains the normal, skew-normal (Azzalini, 1985), skew generalized normal (Arellano-Valle et al., 2004) and skew flexible-normal (Gomez et al., 2011) distributions as special cases. Some important properties of this distribution are establi...

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...

Abstract. The rank of a skew partition λ/μ, denoted rank(λ/μ), is the smallest number r such that λ/μ is a disjoint union of r border strips. Let sλ/μ(1 ) denote the skew Schur function sλ/μ evaluated at x1 = · · · = xt = 1, xi = 0 for i > t. The zrank of λ/μ, denoted zrank(λ/μ), is the exponent of the largest power of t dividing sλ/μ(1 ). Stanley conjectured that rank(λ/μ) = zrank(λ/μ). We sho...

Tutte associates a V by V skew-symmetric matrix T , having indeterminate entries, with a graph G=(V,E). This matrix, called the Tutte matrix, has rank exactly twice the size of a maximum cardinality matching of G. Thus, to find the size of a maximum matching it suffices to compute the rank of T . We consider the more general problem of computing the rank of T +K where K is a real V by V skew-sy...

Let ∇ be a metric connection with totally skew-symmetric torsion T on a Riemannian manifold. Given a spinor field Ψ and a dilaton function Φ, the basic equations in type II B string theory are ∇Ψ = 0 , δ(T) = a · (

Let $S(G^{sigma})$ be the skew-adjacency matrix of the oriented graph $G^{sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $sigma$ to each of its edges. The skew energy of an oriented graph $G^{sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{sigma})$. Two oriented graphs are said to be skew equienergetic iftheir skew energies...

Let ,: X_T+ X be a semiflow on a compact metric space X. A function F: X_T+ X is subadditive with respect to , if F(x, t+s) F(x, t)+F(,(x, t), s). We define the maximal growth rate of F to be supx # X lim supt (1 t) F(x, t). This growth rate is shown to equal the maximal growth rate of the subadditive function restricted to the minimal center of attraction of the semiflow. Applications to Birkh...