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A new class of multivariate distributions: Scale mixture of Kotz-type distributions

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  • Arslan, Olcay

Abstract

This paper proposes a new family of multivariate distributions as the scale mixture of the multivariate Kotz-type distribution and the inverse generalized gamma distribution. Definition and some of the main properties are given. It is shown that the new family belongs to the elliptically contoured distributions family, and as a result of the mixing approach it includes the longer tailed distributions than the Kotz-type distribution. Thus, the new family may be regarded as a useful extension of the Kotz-type distribution for robustness purposes. It is also shown that the multivariate t-distribution and the generalized versions of the multivariate t-distribution introduced by Arellano-Valle and Bolfarine [1995. On some characterizations of the t distribution. Statist Probab. Lett. 25, 79-85.] and Arslan [2004. Family of multivariate generalized t distributions. J. Multivar. Anal. 89, 329-337.] belong to the new family. Therefore, to unify all the standard and generalized versions of the t-distribution we call this new class of the distributions as the "family of t-type distributions".

Suggested Citation

  • Arslan, Olcay, 2005. "A new class of multivariate distributions: Scale mixture of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 18-28, November.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:1:p:18-28
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    References listed on IDEAS

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    1. Arslan, Olcay, 2004. "Family of multivariate generalized t distributions," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 329-337, May.
    2. Haro-López, Rubén A. & Smith, Adrian F. M., 1999. "On Robust Bayesian Analysis for Location and Scale Parameters," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 30-56, July.
    3. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    4. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    5. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
    6. Kotz, Samuel & Nadarajah, Saralees, 2001. "Some extremal type elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 171-182, September.
    7. Kotz, S. & Ostrovskii, I., 1994. "Characteristic Functions of a Class of Elliptic Distributions," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 164-178, April.
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    Cited by:

    1. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.
    2. Fung, Thomas & Seneta, Eugene, 2010. "Extending the multivariate generalised t and generalised VG distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 154-164, January.
    3. Del Brio, Esther B. & Ñíguez, Trino-Manuel & Perote, Javier, 2008. "Multivariate Gram-Charlier Densities," MPRA Paper 29073, University Library of Munich, Germany.
    4. Díaz-García, José A. & Gutiérrez-Jáimez, Ramón, 2011. "Distributions of the compound and scale mixture of vector and spherical matrix variate elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 143-152, January.

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