Advanced SearchSearch Tips
An approximate fitting for mixture of multivariate skew normal distribution via EM algorithm
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
An approximate fitting for mixture of multivariate skew normal distribution via EM algorithm
Kim, Seung-Gu;
  PDF(new window)
Fitting a mixture of multivariate skew normal distribution (MSNMix) with multiple skewness parameter vectors via EM algorithm often requires a highly expensive computational cost to calculate the moments and probabilities of multivariate truncated normal distribution in E-step. Subsequently, it is common to fit an asymmetric data set with MSNMix with a simple skewness parameter vector since it allows us to compute them in E-step in an univariate manner that guarantees a cheap computational cost. However, the adaptation of a simple skewness parameter is unrealistic in many situations. This paper proposes an approximate estimation for the MSNMix with multiple skewness parameter vectors that also allows us to treat them in an univariate manner. We additionally provide some experiments to show its effectiveness.
multivariate skew normal distribution;mixture model;EM algorithm;multivariate normal cdf;
 Cited by
Azzalini, A. (1985). A class of distribution which includes the normal ones, Scandinavian Journal of Statistics, 33, 561-574.

Azzalini, A. and Dalla-Valle, A. (1996). The multivariate skew normal distribution, Biometrika, 83, 715-726. crossref(new window)

Arellano-Valle, R. B. and Genton, M. G. (2005). On fundamental skew distributions, Journal of Multivariate Analysis, 96, 93-116. crossref(new window)

Cabral, C. S., Lachos, V. H., and Prates, M. O. (2012). Multivariate mixture modeling using skew-normal independent distribution, Computational Statistics and Data Analysis, 56, 126-142. crossref(new window)

Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, Wiley, New York.

Ho, H. J., Lin, T. I., Chen, H.-Y., and Wang, W.-L. (2012). Some results on the truncated multivariate t distribution, Journal of Statistical Planning & Inference, 142, 25-40. crossref(new window)

Kim, S.-G. (2014). An alternating approach of maximum likelihood estimation for mixture of multivariate skew t-distribution, The Korean Journal of Applied Statistics, 27, 819-831. crossref(new window)

Lee, S. X. and McLachlan, G. J. (2013). On mixtures of skew normal and skew t-distributions, Advances in Data Analysis and Classification, 7, 241-266. crossref(new window)

Lee, S. X. and McLachlan, G. J. (2014a). Finite mixtures of multivariate skew t-distributions: some recent and new results, Statistics and Computing, 24, 181-202. crossref(new window)

Lee, S. X. and McLachlan, G. J. (2014b). Finite mixtures of canonical fundamental skew t-distributions, arXiv: 1405.0685v1 [Stat. ME] 4 May 2014.

Lin, T.-I. (2010). Robust mixture modeling using multivariate skew t-distributions, Statistics and Computing, 20, 343-356. crossref(new window)

Olson, J. M. and Weissfeld, L. A. (1991). Approximation of certain multivariate integrals, Statistics & Probability Letters, 11, 309-317. crossref(new window)

Pyne, S., Hu, X., Wang, K., Rossin, E., Lin, T. I., Maier, L., Baecher-Allan, C., McLachlan, G. J., Tamayo, P., Hafler, D. A., De Jager, P. L., and Mesirov, J. P. (2009). Automated high-dimensional flow cytometric data analysis, In Proceedings of the National Academy of Sciences, 106 , 8519-8524. crossref(new window)

Sahu, S. K., Dey, D. K., and Branco, M. D. (2003). A new class of multivariate skew distribution with application to Bayesian regression model, The Canadian Journal of Statistics, 31, 129-150. crossref(new window)