The aim of this paper is to consider the SN class of distributions as a member of a broader class of distributions, introducing another structural parameter. The starting point is the study of the Normal curves of the r-th order, (Box, 1953), (Turner, 1960), (Vianelli, 1963), considered also in Azzalini (1986). The arrival point showed in this paper is the obtaining of the exponential family generated by the skew-normal distribution, through the method of exponential tilting introduced by Efron (1981). We proved that this family is an example of extended SN distribution as introduced by Azzalini (1985).

The exponential family generated by the skew-normal distribution.

Dalla Valle, Alessandra
2002

Abstract

The aim of this paper is to consider the SN class of distributions as a member of a broader class of distributions, introducing another structural parameter. The starting point is the study of the Normal curves of the r-th order, (Box, 1953), (Turner, 1960), (Vianelli, 1963), considered also in Azzalini (1986). The arrival point showed in this paper is the obtaining of the exponential family generated by the skew-normal distribution, through the method of exponential tilting introduced by Efron (1981). We proved that this family is an example of extended SN distribution as introduced by Azzalini (1985).
File in questo prodotto:
File Dimensione Formato  
WP_2002_13.pdf

accesso aperto

Licenza: Non specificato
Dimensione 35.49 MB
Formato Adobe PDF
35.49 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3442316
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact