Mean of skew-normal distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg61877] Mean of skew-normal distribution
- From: "Valeri Astanoff" <astanoff at yahoo.fr>
- Date: Thu, 3 Nov 2005 04:58:46 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Dear group, I want to prove with help of mathematica [5.1] that this integral : Integrate[x*(1+Erf[(\[Lambda]*(x-\[Mu]))/ (Sqrt[2]*\[Sigma])])/(E^((x-\[Mu])^2/(2*\[Sigma]^2))* (Sqrt[2*Pi]*\[Sigma])),{x,-Infinity,Infinity}] - 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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