In this paper, we compute doubly truncated moments for the selection elliptical class of distributions, including some multivariate asymmetric versions well-known such as normal, Student’s t, slash, among others. We address members family, establishing neat formulation high-order and its first two moments. establish sufficient necessary conditions existence these Further, propose optimized meth...

Quantifying dependence between extreme values is a central problem in many theoretical and applied studies. The main distinction is between asymptotically independent and asymptotically dependent extremes, with important theoretical examples of these general limiting classes being the extremal behaviour of a bivariate Normal distribution, for asymptotic independence, and of the bivariate t dist...

An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, $A^T=A^{-1}$, respectively. We give necessary sufficient conditions on a complex so that it sum of type ``"orthogonal $+$ symmetric" in terms the Jordan form $A-A^T$. also "orthogonal skew-symmetric" $A+A^T$.

Abstract. In this paper, a family of skew-slash distributions is defined and investigated. We define the new family by the scale mixture of a skew-elliptically distributed random variable with the power of a uniform random variable. This family of distributions contains slash-elliptical and skew-slash distributions. We obtain the moments and some distributional properties of the new family of d...

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

Robin Harte and David Larson The first author was partially supported by Enterprise Ireland grant number IC/2001/027 Abstract We offer a perturbation theory for finite ascent and descent properties of bounded operators. There are various degrees of “skew exactness” ([10];[7] (10.9.0.1), (10.9.0.2)) between compatible pairs of operators, bounded and linear between normed spaces: 1. Definition Su...

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Severa...

The Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) type models have become important tools in financial application since their ability to estimate the volatility of time series data. In empirical literature, presence skewness and heavy-tails impacts on how well GARCH-type able capture market sufficiently. This study estimates asset returns based GARCH(1,1) model assuming Ske...