A note on the likelihood and moments of the skew-normal distribution
In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that th...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2008 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2099/8944 |
| Online Access: | https://hdl.handle.net/2099/8944 |
| Access Level: | Open access |
| Keyword: | Mathematical statistics Numerical analysis--Simulation methods Stochastic differential equations--Numerical solutions Skew-normal distribution Maximum likelihood equations Moments Estadística matemàtica Anàlisi numèrica Classificació AMS::62 Statistics::62F Parametric inference Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Summary: | In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting. |
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