, Volume 69, Issue 3, pp 279–295 | Cite as

Statistical aspects of the scalar extended skew-normal distribution



This paper presents some inferential results about the extended skew-normal family in the scalar case. For this family many inferential aspects are still unexplored. The expected information matrix is obtained and some of its properties are discussed. Some simulation experiments and an application to real data are presented pointing out not infrequent estimation problems such as different estimates in function of the starting values of the algorithm which leads to substantially equivalents densities. All these issues underline a problem of near unidentifiability.


Extended skew-normal distribution Information matrix Skew-normal distribution 


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  1. Arnold, B. C. and Beaver, R. J. (2000) Hidden truncation model, Sankhyã, series A, 62, 22–35.MathSciNetGoogle Scholar
  2. Arnold, B. C., Beaver, R. J., Groeneveld, R. A. and Meeker, W. Q. (1993) The non truncated marginal of a truncated bivariate normal distribution, Psychometrika, 58, 471–488.MathSciNetMATHCrossRefGoogle Scholar
  3. Azzalini, A. (1985) A class of distributions which includes the normal ones, Scand. J. Statist., 12, 171–178.MathSciNetMATHGoogle Scholar
  4. Capitanio, A., Azzalini, A. and Stanghellini, E. (2003) Graphical models for skew-normal variates, Scand. J. Statist., 30, 129–144.MathSciNetCrossRefGoogle Scholar
  5. Gupta, S. S. and Pillai, K. C. S. (1965) On linear functions of ordered correlated normal random variables, Biometrika, 53, 367–379.MathSciNetGoogle Scholar
  6. Mardia, K. V. (1970) Measures of multivariate skewness and kurtosis with applications, Biometrika, 57, 519–530.MathSciNetMATHCrossRefGoogle Scholar
  7. Owen, D. B. (1956) Tables for computing bivariate normal probabilities, Ann. Math. Statist., 27, 1075–1090.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Sapienza Università di Roma 2011

Authors and Affiliations

  1. 1.Dip. Sc. StatisticheUniversità di PadovaPadovaItalia

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