Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Some results on the scalar Skew-normal distribution

  • Published:
Journal of the Italian Statistical Society Aims and scope Submit manuscript

Summary

Miscellaneous results about basic properties of the scalar Skew-normal distribution are presented. In particular, some recurrence relations on incomplete moments are derived and some results on moments of order statistics are illustrated. Moreover, some results on probability transformations are introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aigner, D. J., Lovell, C. A. K., Schmidt, P. (1977), Formulation and estimation of stochastic frontier production function model.J. Economet., 12, 21–37.

    Article  MathSciNet  Google Scholar 

  • Arnold, B. C., Beaver, R. J., Groeneveld, R. A., Meeker, W. Q. (1993), The nontruncated marginal of a truncated bivariate normal distribution.Psychometrica, 58, 471–478.

    Article  MATH  MathSciNet  Google Scholar 

  • Azzalini, A. (1985), A class of distributions which includes the Normal ones.Scand. J. Statist., 12, 171–178.

    MATH  MathSciNet  Google Scholar 

  • Azzalini, A. (1986), Further results on a class of distributions which includes the normal ones.Statistica, 2, 199–208.

    MathSciNet  Google Scholar 

  • Azzalini, A., Della Valle, A. (1996), The multivariate Skew-normal distribution.Biometrika, 2, 715–726.

    Article  Google Scholar 

  • Balakrishnan, N., Clifford Cohen, A. (1991),Order statistics and Inference. Academic Press, Inc., San Diego, CA.

    MATH  Google Scholar 

  • Copas, J. B., Li, H. G. (1997), Inference for non-random samples (with discussion).J. Roy. Stat. Soc., 59, 55–95.

    Article  MATH  MathSciNet  Google Scholar 

  • Di Ciccio, T., Kass, R., Raftery, A., Wasserman, L. (1997), Computing Bayes factors by combining simulation and asymptotic approximations.J. Am. Stat. Ass., 92, 903–915.

    Article  Google Scholar 

  • Elandt, R. C. (1961), The folded normal distribution: two methods of estimating parameters from moments.Technometrics, 3, 551–562.

    Article  MATH  MathSciNet  Google Scholar 

  • Frisch, R. (1925), Recurrence formulae for moments of the point binomial.Biometrika, 17, 165.

    MATH  Google Scholar 

  • Henze, N. (1986), Aprobabilistic representation of the Skew-normal distribution.Scand. J. Statist., 13, 271–275.

    MATH  MathSciNet  Google Scholar 

  • Liseo, B. (1990), The skew-normal class of densities: inferential aspects from a bayesian viewpoint.Statistica, 50, 59–70 (in Italian).

    Google Scholar 

  • Mukhopadhyay, S., Vidakovic, B. (1995), Efficiency of linear Bayes rules for a normal mean: skewed prior class.The Statistician, 44, 389–397.

    Article  Google Scholar 

  • Owen, D. B. (1956), Tables for computing bivariate normal probabilities.Ann. Math. Statist., 27, 1075–1090.

    Article  MATH  MathSciNet  Google Scholar 

  • Ruben, H. (1954), On the moments of order statistics in samples from normal populations.Biometrika, 41, 200–227.

    MATH  MathSciNet  Google Scholar 

  • Salvan, A. (1986), Locally most powerful invariant test of normality.Atti XXXIII Riunione Società Italiana di Statistica, 2, 173–179 (in Italian).

    Google Scholar 

  • Shohat, J. A., Tamarkin, J. D. (1943),The problem ofmoments. New York: Amer. Math. Soc.

    Google Scholar 

  • Stuart, A., Ord, J. K. (1994),Kendall’s Advanced Theory of Statistics. Vol. 1, Sixth Edition, London: Edward Arnold.

    Google Scholar 

  • Zacks, S. (1981),Parametric Statistical Inference. Oxford: Pergamo: Press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chiogna, M. Some results on the scalar Skew-normal distribution. J. Ital. Statist. Soc. 7, 1 (1998). https://doi.org/10.1007/BF03178918

Download citation

  • DOI: https://doi.org/10.1007/BF03178918

Keywords