Multivariate Pearson type II distribution : statistical and mathematical features

• Autorzy: Khalafi M. , Azimmohseni M.
• Języki publikacji: EN

Abstrakty

EN

In this article, we first review the main characterizations of multivariate Pearson type II distribution as a subclass of multivariate symmetric spherical distributions. Then we try to provide specific mathematical and statistical principles underlying the construction of this subclass of multivariate distributions.

Słowa kluczowe

EN

multivariate Pearson type II distribution; hypersphere; complex normal distribution; norm-scale invariant; simulation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 1
• Strony: 119--126
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Khalafi M.

• Department of Statistics, Faculty of Science, Golestan University, P.O. Box 155, Gorgan, Iran

autor

Azimmohseni M.

• Department of Statistics, Faculty of Science, Golestan University, P.O. Box 155, Gorgan, Iran

Bibliografia

• [1] R. B. Arellano-Valle, On some characterizations of spherical distributions, Statist. Probab. Lett. 54 (2001), pp. 227-232.
• [2] R. B. Arellano-Valle and H. Bolfarine, On some characterizations of the t-distribution, Statist. Probab. Lett. 25 (1995), pp. 79-85.
• [3] K.-T. Fang, S. Kotz, and K.-W. Ng, Symmetric Multivariate and Related Distributions, Chapman and Hall, London 1990.
• [4] N. R. Goodman, Statistical analysis based on a certain multivariate complex Gaussian distribution (An introduction), Ann. Math. Statist. 34 (1) (1963), pp. 152-177.
• [5] G. Guralnik, C. Zemach, and T. Warnock, An algorithm for uniform random sampling of points in and on a hypersphere, Inform. Process. Lett. 21 (1985), pp. 17-21.
• [6] N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Volume 2, second edition, Wiley, New York 1994.
• [7] J. J. Liang and P. M. Bentler, Characterizations of some subclasses of spherical distributions, Statist. Probab. Lett. 40 (1998), pp. 155-164.
• [8] G. Marsaglia, Choosing a point from the surface of sphere, Ann. Math. Statist. 43 (2) (1972), pp. 645-646.
• [9] M. E. Muller, A note on a method for generating points uniformly on n-dimensional spheres, Commn. ACM 2 (4) (1959), pp. 19-20.
• [10] S. M. Ross, Simulation, Fourth Edition (Statistical Modeling and Decision Science), Elsevier Inc., 2006.
• [11] R. Y. Rubinstein and D. P. Kroese, Simulation and Monte Carlo Methods, second edition, Wiley, 2008.
• [12] N. A. Volodin, Spherically symmetric logistic distribution, J. Multivariate Anal. 70 (1999), pp. 202-206.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).