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On the infinite divisibility of some skewed symmetric distributions

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  • Domínguez-Molina, J. Armando
  • Rocha-Arteaga, Alfonso

Abstract

Infinite divisibility of some symmetric distributions skewed by an additive component is investigated. We find in particular that the skew-normal distribution of Azzalini [1985. A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178] and the multivariate skew-normal distribution of Azzalini and Dalla Valle [1996. The multivariate skew-normal distribution. Biometrika 83, 715-726] are not infinitely divisible.

Suggested Citation

  • Domínguez-Molina, J. Armando & Rocha-Arteaga, Alfonso, 2007. "On the infinite divisibility of some skewed symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 644-648, March.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:6:p:644-648
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    References listed on IDEAS

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    1. Horn, Roger A. & Steutel, F. W., 1978. "On multivariate infinitely divisible distributions," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 139-151, January.
    2. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
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    Cited by:

    1. A. Abtahi & J. Behboodian & M. Sharafi, 2012. "A general class of univariate skew distributions considering Stein’s lemma and infinite divisibility," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 193-206, February.
    2. Hossein Negarestani & Ahad Jamalizadeh & Sobhan Shafiei & Narayanaswamy Balakrishnan, 2019. "Mean mixtures of normal distributions: properties, inference and application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 501-528, May.
    3. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.

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