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.
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.
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.
Azzalini, A. (1985), A class of distributions which includes the Normal ones.Scand. J. Statist., 12, 171–178.
Azzalini, A. (1986), Further results on a class of distributions which includes the normal ones.Statistica, 2, 199–208.
Azzalini, A., Della Valle, A. (1996), The multivariate Skew-normal distribution.Biometrika, 2, 715–726.
Balakrishnan, N., Clifford Cohen, A. (1991),Order statistics and Inference. Academic Press, Inc., San Diego, CA.
Copas, J. B., Li, H. G. (1997), Inference for non-random samples (with discussion).J. Roy. Stat. Soc., 59, 55–95.
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.
Elandt, R. C. (1961), The folded normal distribution: two methods of estimating parameters from moments.Technometrics, 3, 551–562.
Frisch, R. (1925), Recurrence formulae for moments of the point binomial.Biometrika, 17, 165.
Henze, N. (1986), Aprobabilistic representation of the Skew-normal distribution.Scand. J. Statist., 13, 271–275.
Liseo, B. (1990), The skew-normal class of densities: inferential aspects from a bayesian viewpoint.Statistica, 50, 59–70 (in Italian).
Mukhopadhyay, S., Vidakovic, B. (1995), Efficiency of linear Bayes rules for a normal mean: skewed prior class.The Statistician, 44, 389–397.
Owen, D. B. (1956), Tables for computing bivariate normal probabilities.Ann. Math. Statist., 27, 1075–1090.
Ruben, H. (1954), On the moments of order statistics in samples from normal populations.Biometrika, 41, 200–227.
Salvan, A. (1986), Locally most powerful invariant test of normality.Atti XXXIII Riunione Società Italiana di Statistica, 2, 173–179 (in Italian).
Shohat, J. A., Tamarkin, J. D. (1943),The problem ofmoments. New York: Amer. Math. Soc.
Stuart, A., Ord, J. K. (1994),Kendall’s Advanced Theory of Statistics. Vol. 1, Sixth Edition, London: Edward Arnold.
Zacks, S. (1981),Parametric Statistical Inference. Oxford: Pergamo: Press.
Author information
Authors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/BF03178918