The Multivariate Extended Skew Normal Distribution and Its Quadratic Forms
نویسندگان
چکیده
In this talk, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, conditional probability density functions and independence are discussed. The definition of extended noncentral skew chi-square distribution is given. The necessary and sufficient conditions under which a quadratic form has an extended noncentral skew chisquare distribution are obtained. For illustration of our main results, several examples are given.
منابع مشابه
Comparing the Efficiency of Dmus with Normal and Skew-Normal Distribution using Data Envelopment Analysis
Data envelopment analysis (DEA) is a nonparametric approach to evaluate theefficiency of decision making units (DMU) using mathematical programmingtechniques. Almost, all of the previous researches in stochastic DEA have been usedthe stochastic data when the inputs and outputs are normally distributed. But, thisassumption may not be true in practice. Therefore, using a normal distribution wi...
متن کاملDistribution of matrix quadratic forms under skew-normal settings
For a class of skew-normal matrix distributions, the density function, moment generating function and independent conditions are obtained. The noncentral skew Wishart distribution is defined and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart distributed random matrix are established. A new version of Cochran’s theorem is given. For illustration, ...
متن کاملOn the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality
It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...
متن کاملAn Extension of the Birnbaum-Saunders Distribution Based on Skew-Normal t Distribution
In this paper, we introducte a family of univariate Birnbaum-Saunders distributions arising from the skew-normal-t distribution. We obtain several properties of this distribution such as its moments, the maximum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstr...
متن کاملApproximating the Distributions of Singular Quadratic Expressions and their Ratios
Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...
متن کامل