Page 432 - Contributed Paper Session (CPS) - Volume 4

CPS2523 Christian E. Galarza et al.
2. Methodology
We denote a random variable by an upper-case letter and its realization
by the correspondent lower case and use boldface letters for vectors and
matrices. Let Ip represent a p×p identity matrix and a ones matrix respectively,
A> be the transpose of A, and |X| = (|X1|. . . . , |Xp|) > mean the absolute value
of each component of the vector X. For multiple integrals, we use the
shorthand notation

a. The extended multivariate skew-normal distribution (ESN)
We say that a p × 1 random vector Y follows a ESN distribution with p × 1
location vector µ, p × p positive definite dispersion matrix Σ, a p×1 skewness
parameter vector λ ∈ R p , and shift parameter τ ∈ R, denoted by Y ∼ ESNp(µ,
Σ,λ, τ ), if its pdf is given by

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