Table 2:

Parameters for MVN and MSN cluster scenarios in the simulation study.

Multivariate Normal: MVN (μ, σ)	Multivariate Skew Normal: MSN (μ,σ,δ)
Clustering Variables
[Xlg,X2g] ~ MVN(μg, Σg)	[X1g,X2g] ~ MSN(μg,Σg,δg)
μ1 = [0.50, 4.00], ${\mathbf{\Sigma }}_1=\left[\begin{array}{ll}3.00\hfill & 0.02\hfill \\ 0.02\hfill & 0.90\hfill \end{array}\right]$	μ1 = [-0.20,18.00], ${\mathbf{\Sigma }}_1=\left[\begin{array}{cc}0.011& -0.013\\ -0.013& 1.42\end{array}\right]$, δ1 = [2.60, 3.90]
μ2 = [14.00, 21.00], ${\mathbf{\Sigma }}_2=\left[\begin{array}{cc}3.00& -0.10\\ -0.10& 1.00\end{array}\right]$	μ2 = [9.00, 23.00], ${\mathbf{\Sigma }}_2=\left[\begin{array}{cc}53.50& -0.99\\ -0.99& 0.17\end{array}\right]$, δ2 = [1.40, -0.30]
μ3 = [23.00, 23.50], ${\mathbf{\Sigma }}_3=\left[\begin{array}{cc}55.10& 1.80\\ 1.80& 0.90\end{array}\right]$	μ3 = [26.00, 24.50], ${\mathbf{\Sigma }}_3=\left[\begin{array}{cc}21.20& -0.24\\ -0.24& 0.13\end{array}\right]$, δ3 = [-0.90, -1.10]
p1 = 0.40, p2 = 0.30, p3 = 0.20	p1 = 0.54, p2 = 0.14, p3 = 0.32
Irrelevant Variables
X3 - MVN(68.00, 287.00)	X3 ~ MSN(0.40, 2.00, 31.00)
X4 - MVN(60.00, 296.00)	X4 ~ MSN(62.00, 292.00,0.00)
Correlated Variables
X5 = X1 + Z1, Z1 ~ MVN(0,60)	X5 = X1 + Z1, Z1 ~ MSN(0.00,60.00,3.00)
X6 = X2 + Z2, Z2 ~ MVN(0,3)	X6 = X1 + Z1, Z1 ~ MSN(0.00,3.00,0.00)