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...

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Detalles Bibliográficos
Autores: Martínez, E. H., Varela, H., Gómez, H. W., Bolfarine, Heleno
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099/8944
Acceso en línea:https://hdl.handle.net/2099/8944
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.