A mixture of coalesced generalized hyperbolic distributions

Author
Tortora, Cristina
Franczak, Brian
Browne, Ryan P.
McNicholas, Paul D.
Faculty Advisor
Date
2019
Keywords
clustering , coalesced distributions , convexity , finite mixture models , generalized hyperbolic distribution , mixture of mixtures , MM algorithm , multiple scaled distributions
Abstract (summary)
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.
Publication Information
Tortora, C., Franczak, B.C., Browne, R.P., and McNicholas, P.D. (2019), ‘A mixture of coalesced generalized hyperbolic distributions’. Journal of Classification 36(1), 26-57.
DOI
Notes
Item Type
Article
Language
English
Rights
All Rights Reserved