We introduce a formalism for constructing models of the gravitational lens action of arbitrary elliptical surface mass distributions including varying ellipticity and isodensity-twist. The projected elliptical surface mass distributions are cut to slices of constant surface mass density for which the de ection is easy to compute. The de ection of the total mass distribution is found by superpos...

Sérsic (1968) generalized the de Vaucouleurs law which follows the projected (observed) one dimensional radial profile of elliptical galaxies closely and Dehnen (1993) proposed an analytical formula of the 3-dimensional light distributions whose projected line profile resembles the de Vaucouleurs law. This paper is involved to recover the Dehnen model and generalize the model to account for gal...

In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the ta...

In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the ta...

Shannon and Rényi entropies are two important measures of uncertainty for data analysis. These have been studied multivariate Student-t skew-normal distributions. In this paper, we extend the entropy to skew-t finite mixture (FMST) This class flexible distributions allows handling asymmetry tail weight behavior simultaneously. We find upper lower bounds these families. Numerical simulations ill...

The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these...

We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate t distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the mixture, in addition to the location vector and the ...

This paper is a case study of a general method for designing generators of repeatable non-Poisson sequences of pseudorandom pulses. A class of normal distributions and some classes of skew distributions are derived. Block diagrams and design guides are given. The study is based both on analytical and simulation approaches. Applications of the proposed system may be found in the field of hardwar...

This article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions. It is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution, the asymptotic covariance matrix of sample covariances has a structure that results in the retention of ...

In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters + and 7. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators of + and 7. Under the entropy loss and quadratic loss, the best Bayesian estimators of 7 are derived as well. Some applica...