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Characteristic functions of scale mixtures of multivariate skew-normal distributions. (English) Zbl 1221.60020
Summary: We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew-normal distributions. In particular, we describe the characteristic function of skew-normal, skew-\(t\), and other related distributions.

60E10 Characteristic functions; other transforms
62E10 Characterization and structure theory of statistical distributions
60E05 Probability distributions: general theory
Full Text: DOI
[1] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions with formulas, graphs, and mathematical tables, (1972), Dover Publications, Inc. New York · Zbl 0543.33001
[2] Arellano-Valle, R.B.; Azzalini, A., On the unification of families of skew-normal distributions, Scandinavian journal of statistics, 33, 561-574, (2006) · Zbl 1117.62051
[3] Arellano-Valle, R.B.; Branco, M.D.; Genton, M.G., A unified view on skewed distributions arising from selections, The Canadian journal of statistics, 34, 581-601, (2006) · Zbl 1121.60009
[4] Arellano-Valle, R.B.; Genton, M.G., On fundamental skew distributions, Journal of multivariate analysis, 96, 93-116, (2005) · Zbl 1073.62049
[5] Arellano-Valle, R.B.; Genton, M.G., An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators, Annals of the institute of statistical mathematics, 62, 363-381, (2010) · Zbl 1440.62178
[6] Azzalini, A., A class of distributions which includes the normal ones, Scandinavian journal of statistics, 12, 171-178, (1985) · Zbl 0581.62014
[7] Azzalini, A., The skew-normal distribution and related multivariate families (with discussion), Scandinavian journal of statistics, 32, 159-188, (2005), C/R 189-200 · Zbl 1091.62046
[8] Azzalini, A.; Capitanio, A., Statistical applications of the multivariate skew normal distribution, Journal of the royal statistical society, series B, 61, 579-602, (1999) · Zbl 0924.62050
[9] Azzalini, A.; Capitanio, A., Distributions generated by perturbation of symmetry with emphasis on a multivariate skew \(t\) distribution, Journal of the royal statistical society, series B, 65, 367-389, (2003) · Zbl 1065.62094
[10] Azzalini, A.; Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 715-726, (1996) · Zbl 0885.62062
[11] Azzalini, A.; Genton, M.G., Robust likelihood methods based on the skew-\(t\) and related distributions, International statistical review, 76, 106-129, (2008) · Zbl 1206.62102
[12] Bisgaard, T.M.; Sasvári, Z., Characteristic functions and moment sequences, (2000), Nova Science Publishers, Inc. New York
[13] Branco, M.D.; Dey, D.K., A general class of multivariate skew-elliptical distributions, Journal of multivariate analysis, 79, 99-113, (2001) · Zbl 0992.62047
[14] Buckle, D.J., Bayesian inference for stable distributions, Journal of the American statistical association, 90, 605-613, (1995) · Zbl 0826.62020
[15] Genton, M.G., Skew-elliptical distributions and their applications: A journey beyond normality, edited volume, (2004), Chapman & Hall, CRC Boca Raton, FL · Zbl 1069.62045
[16] Henze, N., A probabilistic representation of the skew-normal distribution, Scandinavian journal of statistics, 13, 271-275, (1986) · Zbl 0648.62016
[17] S. Hurst, The characteristic function of the Student \(t\)-distribution, in: Financial Mathematics Research Report 006-95, Australian National University, Canberra ACT 0200, Australia, 1995.
[18] Kotz, S.; Nadarajah, S., Multivariate t distributions and their applications, (2004), Cambridge University Press Cambridge · Zbl 1100.62059
[19] Kozubowski, T.J.; Podgórski, K., Skew Laplace distributions. I. their origins and inter-relations, Mathematical scientist, 33, 22-34, (2008) · Zbl 1167.62014
[20] Lachos, V.H.; Dey, D.K.; Cancho, V.G., Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective, Journal of statistical planning and inference, 139, 4098-4110, (2009) · Zbl 1183.62048
[21] Lukacs, E., Characteristic functions, (1970), Griffin London · Zbl 0201.20404
[22] Lukacs, E., Developments in characteristic function theory, (1983), Macmillan Publishing Co., Inc. New York · Zbl 0515.60022
[23] Nelson, P.R., An approximation for the complex normal probability integral, BIT numerical mathematics, 22, 94-100, (1982) · Zbl 0486.30023
[24] Pewsey, A., The wrapped skew-normal distribution on the circle, Communications in statistics—theory and methods, 29, 2459-2472, (2000) · Zbl 0992.62048
[25] Samorodnitsky, G.; Taqqu, M.S., Stable non-Gaussian random processes, (1994), Chapman and Hall New York · Zbl 0925.60027
[26] Steck, G.P.; Owen, B., A note on the equicorrelated multivariate normal distribution, Biometrika, 49, 269-271, (1962) · Zbl 0112.11110
[27] Wang, J.; Genton, M.G., The multivariate skew-slash distribution, Journal of statistical planning and inference, 136, 209-220, (2006) · Zbl 1081.60013
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