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Mean of skew-normal distribution

  • To: mathgroup at
  • Subject: [mg61877] Mean of skew-normal distribution
  • From: "Valeri Astanoff" <astanoff at>
  • Date: Thu, 3 Nov 2005 04:58:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Dear group,

I want to prove with help of mathematica [5.1] that this integral :


 - which is the mean of a so-called skew-normal distribution -
is equal to :

\[Mu] + (Sqrt[2]*\[Lambda]*\[Sigma])/Sqrt[Pi(1 + \[Lambda]^2)]

Series expanding with lambda near 0 shows
that it is true at any order, but of course
that's not a proof, and I shall be grateful
to the good Samaritan that will help me. 

Valeri Astanoff

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