Robust finite mixture modeling of multivariate unrestricted skew-normal generalized hyperbolic distributions
- 157 Downloads
In this paper, we introduce an unrestricted skew-normal generalized hyperbolic (SUNGH) distribution for use in finite mixture modeling or clustering problems. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families such as the scale mixtures of skew-normal, the skew-normal generalized hyperbolic and its corresponding symmetric versions. The class of distributions provides a much needed unified framework where the choice of the best fitting distribution can proceed quite naturally through either parameter estimation or by placing constraints on specific parameters and assessing through model choice criteria. The class has several desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. We illustrate the flexibility of the proposed class of distributions in a mixture modeling context using a Bayesian framework and assess the performance using simulated and real data.
KeywordsBayesian analysis Finite mixtures MCMC Unrestricted skew-normal generalized hyperbolic family Skew-normal Generalized hyperbolic distribution
The authors would like to thank the coordinating editor and anonymous reviewers for their suggestions, corrections and encouragement, which helped us to improve earlier versions of the manuscript.
- Azzalini, A.: Package ‘sn’. http://azzalini.stat.unipd.it/SN (2015). Accessed 13 May 2017
- Azzalini, A., with the collaboration of Capitanio, A.: The Skew-Normal and Related Families. IMS Monographs Series. Cambridge University Press (2014)Google Scholar
- Barndorff-Nielsen, O., Blaesild, P.: Hyperbolic distributions. In: Kotz, S., Johnson, N.L., Read, C. (eds.) Encyclopedia of Statistical Sciences, vol. 3. Wiley, New York (1980)Google Scholar
- Morris, K., McNicholas, P.D., Punzo, A., Browne, R.P.: Robust Asymmetric Clustering. ArXiv e-print arxiv:1402.6744 (2014)
- R Core Team.: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/ (2017). Accessed 20 June 2017
- Seshadri, V.: The Inverse Gaussian Distribution: A Case Study in Exponential Families. Oxford University Press, New York (1993)Google Scholar
- Wang, K., Ng, S.K., McLachlan, G.J.: Multivariate skew t mixture models: applications to fluorescence-activated cell sorting data. In: Digital Image Computing: Techniques and Applications, Los Alamitos, California, pp. 526–531. IEEE (2009)Google Scholar