Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables | Zendy

Maximiano Pinheiro | Zendy

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Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables

Author(s) -

Maximiano Pinheiro

Publication year - 2012

Publication title -

journal of probability and statistics

Language(s) - English

Resource type - Journals

eISSN - 1687-9538

pISSN - 1687-952X

DOI - 10.1155/2012/758975

Subject(s) - mathematics , marginal distribution , affine transformation , joint probability distribution , subclass , multivariate normal distribution , invertible matrix , random variable , multivariate statistics , property (philosophy) , skew , convolution of probability distributions , combinatorics , pure mathematics , statistics , probability mass function , computer science , philosophy , epistemology , antibody , immunology , biology , telecommunications

Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by non-singular affine transformations of vectors of independent two-piece normal variables, the most important subclass of Ferreira and Steel’s general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of Arellano-Valle and Azzalini’s unified skew-normal densities and then using the property of closure under marginalization of the latter class.

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