A Mixture of Coalesced Generalized Hyperbolic Distributions

Cristina Tortora (), Brian C. Franczak (), Ryan P. Browne () and Paul D. McNicholas ()
Additional contact information
Cristina Tortora: San José State University
Brian C. Franczak: MacEwan University
Ryan P. Browne: University of Waterloo
Paul D. McNicholas: McMaster University

Journal of Classification, 2019, vol. 36, issue 1, No 3, 26-57

Abstract: Abstract A mixture of multiple scaled generalized hyperbolic distributions (MMSGHDs) is introduced. Then, a coalesced generalized hyperbolic distribution (CGHD) is developed by joining a generalized hyperbolic distribution with a multiple scaled generalized hyperbolic distribution. After detailing the development of the MMSGHDs, which arises via implementation of a multi-dimensional weight function, the density of the mixture of CGHDs is developed. A parameter estimation scheme is developed using the ever-expanding class of MM algorithms and the Bayesian information criterion is used for model selection. The issue of cluster convexity is examined and a special case of the MMSGHDs is developed that is guaranteed to have convex clusters. These approaches are illustrated and compared using simulated and real data. The identifiability of the MMSGHDs and the mixture of CGHDs are discussed in an appendix.

Keywords: Clustering; Coalesced distributions; Convexity; Finite mixture models; Generalized hyperbolic distribution; Mixture of mixtures; MM algorithm; Multiple scaled distributions (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00357-019-09319-3

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