Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering. (English) Zbl 1403.62028
Summary: A hidden truncation hyperbolic (HTH) distribution is introduced and finite mixtures thereof are applied for clustering. A stochastic representation of the HTH distribution is given and a density is derived. A hierarchical representation is described, which aids in parameter estimation. Finite mixtures of HTH distributions are presented and their identifiability is proved. The convexity of the HTH distribution is discussed, which is important in clustering applications, and some theoretical results in this direction are presented. The relationship between the HTH distribution and other skewed distributions in the literature is discussed. Illustrations are provided – both of the HTH distribution and application of finite mixtures thereof for clustering.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62H12 | Estimation in multivariate analysis |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
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