International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Skew-Normal Distribution

  • Adelchi Azzalini
Reference work entry
In its simplest reading, the term “skew-normal” refers to a family of continuous probability distributions on the real line having density function of form
$$\phi (z;\alpha ) = 2\:\phi (z)\;\Phi (\alpha z),\qquad (-\infty <z <\infty ),$$
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References and Further Reading

  1. Arnold BC, Beaver RJ (2000) Hidden truncation models. Sankhyā A 62(1):22–35MathSciNetGoogle Scholar
  2. Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12:171–178MathSciNetMATHGoogle Scholar
  3. Azzalini A (1986) Further results on a class of distributions which includes the normal ones. Statistica 46(2):199–208MathSciNetMATHGoogle Scholar
  4. Azzalini A (2005) The skew-normal distribution and related multivariate families (with discussion) Scand J Stat 32:159–188 (C/R 189–200)Google Scholar
  5. Azzalini A, Capitanio A (1999) Statistical applications of the multivariate skew normal distribution. J R Stat SocB 61(3):579–602 Full version of the paper at (No. 0911.2093)
  6. Azzalini A, Dalla Valle A (1996) The multivariate skew-normal distribution. Biometrika 83:715–726MathSciNetMATHGoogle Scholar
  7. Capitanio A, Azzalini A, Stanghellini E (2003) Graphical models for skew-normal variates. Scand J Statist 30:129–144MathSciNetGoogle Scholar
  8. Chiogna M (1998) Some results on the scalar skew-normal distribution. J Ital Stat Soc 7:1–13Google Scholar
  9. Henze N (1986) A probabilistic representation of the ‘skew-normal’ distribution. Scand J Stat 13:271–275MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Adelchi Azzalini
    • 1
  1. 1.University of PaduaPaduaItaly