Mixtures of Multiple Scaled Generalized Hyperbolic Distributions

• Activity Number: 614
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Cristina Tortora*+ and Ryan P. Browne and Paul D. McNicholas and Brian Franczak
• Companies: McMaster University and University of Guelph and University of Guelph and University of Guelph
• Keywords: model based clustering ; generalized hyperbolic distribution ; mixture models ; scaled mixture ; scale matrix decomposition ; EM-algorithm

Abstract

Model-based clustering considers the overall population as a mixture of groups and each component of this mixture is modeled through its conditional probability distribution. Recently, the mixture of generalized hyperbolic distributions has been proposed. It is able to handle skewness and heavy tails and has the Gaussian, Student-t, normal inverse Gaussian and variance-gamma distributions as special cases. In the present work we propose a mixture of multiple scaled generalized hyperbolic distributions in which the density is estimated using P independent generalized inverse Gaussian distributions. Specifically, we employ the use of the eigen-value decomposition of the component scale matrices to facilitate a multi-dimensional distributed weight variable. This work extends the family of multiple scaled distributions introduced in Forbes and Wraith (2013), to skewed distributions. The present talk will show the results on simulated and real data sets.