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Języki publikacji
Abstrakty
In this paper, we introduce a new family of multivariate distributions, called the unified weighted family, as a generalization to the skew-elliptical family. We study some properties of the proposed family and show that it subsumes many important subfamilies such as the families arisen from the selection and hidden truncation ideas. Although the proposed family is very general, we focus on the multivariate weighted normal family which is regarded as a promising candidate in statistical inference.
Czasopismo
Rocznik
Tom
Strony
215--235
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Department of Mathematics, Statistics and Physics, University of Qatar, Doha, Qatar
- Department of Statistics, Yarmouk University, Irbid, Jordan
autor
- Department of Mathematics, Sharjah University, Sharjah, UAE
autor
- Department of Statistics, Yarmouk University, Irbid, Jordan
Bibliografia
- [1] R. J. Adler, The Geometry of Random Field, Wiley, New York 1981.
- [2] T. T. Alodat, A generalized multivariate skew-normal distribution with application to spatial and regression predictions, M.Sc. Thesis, Department of Statistics, Yarmouk University, Jordan, 2009.
- [3] R. B. Arellano-Valle and A. Azzalini, On the unification of families of skew-normal distributions, Scand. J. Statist. 33 (2006), pp. 561-574.
- [4] R. B. Arellano-Valle, M. D. Branco, and M. G. Genton, A unified view on skewed distributions arising from selection, Canad. J. Statist. 34 (4) (2006), pp. 581-601.
- [5] R. B. Arellano-Valle and M. G. Genton, On fundamental skew distributions, J. Multivariate Anal. 96 (2005), pp. 93-116.
- [6] R. B. Arellano-Valle and M. G. Genton, An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators, Ann. Inst. Statist. Math. 62 (2010), pp. 363-381.
- [7] R. B. Arellano-Valle and M. G. Genton, Multivariate unified skew-elliptical distributions, Chil. J. Stat. 1 (1) (2010), pp. 17-33.
- [8] B. C. Arnold and R. J. Beaver, Hidden truncation models, Sankhya A 62 (2000), pp. 22-35.
- [9] A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171-178.
- [10] A. Azzalini, The skew-normal distribution and related multivariate families, Scand. J. Statist. 32 (2005), pp. 159-188.
- [11] A. Azzalini and A. Capitanio, Statistical applications of the multivariate skew-normal distribution, J. R. Stat. Soc. Ser. B 61 (3) (1999), pp. 579-602.
- [12] A. Azzalini and A. Capitanio, Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution, J. R. Stat. Soc. Ser. B 65 (2) (2003), pp. 367-389.
- [13] A. Azzalini and A. Dalla Valle, The multivariate skew-normal distribution, Biometrika 38 (1996), pp. 715-726.
- [14] A. Capitanio, A. Azzalini, and E. Stanghellini, Graphical models for skew-normal variates, Scand. J. Statist. 30 (2003), pp. 129-144.
- [15] J. A. Domínguez-Molina, G. González-Farias, and A. Gupta, The multivariate closed skew normal distribution, Technical Report 03-12, Department of Mathematics and Statistics, Bowling Green State University, USA, 2003, p. 21.
- [16] M. Ganjali, T. Baghfalahki, and M. Khazaie, A linear mixed model for analyzing longitudinal skew-normal responses with random dropout, J. Korean Statist. Soc. 42 (2013), pp. 149-160.
- [17] G. González-Farias, J. A. Domínguez-Molina, and A. K. M. Gupta, The closed skew-normal distribution, in: Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, M. G. Genton (Ed.), Chapman and Hall/CRC, 2004.
- [18] A. K. Gupta and W. J. Huang, Quadratic forms in skew normal variates, J. Math. Anal. Appl. 273 (2002), pp. 558-564.
- [19] H.-J. Kim, A class of weighted multivariate normal distributions and its properties, J. Multivariate Anal. 99 (2008), pp. 1758-1771.
- [20] H.-J. Kim, A class of weighted multivariate elliptical models useful for robust analysis of nonnormal and bimodal data, J. Korean Statist. Soc. 39 (2010), pp. 83-92.
- [21] A. M. Mathai and S. B. Provost, Quadratic Forms in Random Variables: Theory and Applications, Marcel Dekker, New York 1992.
- [22] K. Podgórski and I. Rychlik, Envelope crossing distributions for Gaussian fields, Probab. Engineering Mechanics 23 (2008), pp. 364-377.
- [23] V. Raluca, On the multivariate skew-normal distribution and its scale mixtures, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 13 (2) (2005), pp. 83-96.
- [24] J. Rodrigues, A Bayesian inference for the extended skew-normal measurement error model, Braz. J. Probab. Stat. 20 (2006), pp. 179-190.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-89c904c6-50d6-42d6-a3c9-24fc022a0c7c