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The Skew Normal Density Function

parameter C
0
Mean:
E(x)
=
2
π
δ
=
0
Variance:
Var(x)
=
1-
2
2
δ
π
=
1
Skewness:
γ
1
=
(4-π)
3
E(x)
2
3/2
Var(x)
=
0
Kurtosis:
γ
2
=
2(-3+π)
4
E(x)
2
Var(x)
=
0
where
δ
=
c
1+
2
c
The skew normal distribution is an extention of the normal distribution. The difference is the presence of skewness, determined by the parameter
C
(for
C=0
we have the normal distribution).

Details

The skew normal density function is given by
Sk(x)=2ϕ(x)Φ(cx)
,
where
ϕ(x)
is the probability density function of the standard normal distribution and
Φ(x)
is its distribution function.
A. Azzalini, "A Class of Distributions Which Includes the Normal Ones," Scandinavian Journal of Statistics, 12(2), 1985 pp. 171–178.

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