Item

Description

Expression

1

E(X)

μ + β δ 2 1 + δ γ

2

var(X)

δ 2 ( γ + α 2 δ ) γ ( 1 + δ γ ) 2

3

Skewness, γ 1

3 β δ 3 γ 2 + α 2 δ γ + ( β δ γ 2 + α 2 δ γ ) 3

4

Excess Kurtosis, γ 2

3 [ α 4 ( 1 + δ γ ) 2 + 2 δ γ ( α 4 ( 1 + 2 δ γ ) γ 3 ( γ + 2 α 2 δ ) ) ] δ γ 3 ( γ + α 2 δ ) 2