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Abstract

Wang, Li and Gupta [] first introduced the skew chi-square distribution based on the multivariate skew normal distribution provided by Azzalini [], and Ye, Wang and Gupta [] extended this results into the skew Wishart distribution. Motivated by these results, we first study a new type of multivariate skew normal distribution introduced by Gupta and Chen [], the moment generating function, independence and quadratic form are discussed, and also a new type of skew chi-square distribution was introduced. Later on, we defined a new type of skew Wishart distribution based on the matrix skew normal models introduced by Ning []. In the end, we will study the probabilistic representation of multivariate skew elliptical models.

Abstract

In this paper, the scale mixtures of multivariate skew slash distributions is introduced. The probability density function with some additional properties are discussed. The first four order moments, skewness and kurtosis of this distribution are calculated. Furthermore, the first two moments of its quadratic forms are obtained. In particular, the linear transformation, stochastic representation and hierarchical representation are studied. In the end, the EM algorithm is proposed.

conditional, This research was partially supported by the KBN 511/2 /91 grant. Key words and phrases: conditional specification, conditional distribution, regression function, conditional Poisson law, bivariate Poisson conditionals distribution. A MS (1980) subject classification: 62H05, 62E10. 238 J. W e s o l o w s k i Ahsanullah and Wesolowski [1] character izat ion of the bivariate normal i ty by the normal conditional distr ibution and the linear m, Wesolowski [1*2] uniqueness theorems for power series conditional distribution and a con- sistent m. In this

function H is best characterized by a unique function -a bivariate copula C, defined everywhere on the unit square 12 by the following relation H(x,y) = C(F(x),G(y)), x)2/GR (see Sklar's Theorem, Sklar (1959)). A bivariate copula is a bivariate cu- mulative distribution function with uniform margins on the unit interval I. 2000 Mathematics Subject Classification: 62E10, 62H05. Key words and phrases: Copulas, positive quadrant dependence, regression, charac- terizing theorems, Lancaster probabilities, diagonal expansion of bivariate density, or- thonormal polynomials