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A hidden truncation hyperbolic (HTH) distribution is introduced and finitemixtures thereof are applied for clustering. A stochastic representation of theHTH distribution is given and a density is derived. A hierarchicalrepresentation is described, which aids in parameter estimation. Finitemixtures of HTH distributions are presented and their identifiability isproved. The convexity of the HTH distribution is discussed, which is importantin clustering applications, and some theoretical results in this direction arepresented. The relationship between the HTH distribution and other skeweddistributions in the literature is discussed. Illustrations are provided ---both of the HTH distribution and application of finite mixtures thereof forclustering.

Hidden Truncation Hyperbolic Distributions, Finite Mixtures Thereof, and Their Application for Clustering