MultiStatM (version 2.1.0)

EVSKSkewt: EVSK multivariate Skew-t

Description

Computes the theoretical values of the mean, variance, skewness and (excess) kurtosis vectors for the d-variate Skew-t distribution \(St_d(\xi, \boldsymbol{\Omega}, \boldsymbol{\alpha},m)\) defined as $$Y = \xi + \sqrt{\frac{m}{S^2}} \mathbf{X}$$ where \(\mathbf{X}\) is a multivariate skew-normal random variable \(SN_d(0, \boldsymbol{\Omega} , \boldsymbol{\alpha})\) and \(S^2\) is a \(\chi^2_m\) random variable independent of \(\mathbf{X}\).

Usage

EVSKSkewt(xi, omega, alpha, m)

Value

A list of theoretical values for the mean, variance, skewness and kurtosis vectors

Arguments

xi

A mean vector

omega

A \(d \times d\) correlation matrix

alpha

shape parameter d-vector

m

degrees of freedom

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021 p.277

S. R. Jammalamadaka, E. Taufer, Gy. Terdik. On multivariate skewness and kurtosis. Sankhya A, 83(2), 607-644.

See Also

Other Moments and cumulants: Cum2Mom(), EVSKGenHyp(), EVSKSkewNorm(), EVSKUniS(), Mom2Cum(), MomCumCFUSN(), MomCumGenHyp(), MomCumMVt(), MomCumSkewNorm(), MomCumUniS(), MomCumZabs()

Examples

xi <- c(0,0,0) #
alpha <- c(10,5,0) #
omega <- diag(3) #
m <- 10 #

EVSKSkewt(xi,omega,alpha,m)