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Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering

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  • Murray, Paula M.
  • Browne, Ryan P.
  • McNicholas, Paul D.

Abstract

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.

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  • Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    • Handle: RePEc:eee:jmvana:v:161:y:2017:i:c:p:141-156
    DOI: 10.1016/j.jmva.2017.07.008
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    Cited by:

    1. Wei, Yuhong & Tang, Yang & McNicholas, Paul D., 2019. "Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 18-41.
    2. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    3. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Michael P. B. Gallaugher & Paul D. McNicholas, 2020. "Mixtures of skewed matrix variate bilinear factor analyzers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 415-434, June.
    5. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    6. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2019. "Note of Clarification on ‘Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering’, by Murray, Browne, and McNicholas, J. Multivariate Anal. 161 (2017," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 475-476.
    7. Lee, Sharon X. & McLachlan, Geoffrey J., 2021. "On formulations of skew factor models: Skew factors and/or skew errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    8. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    9. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.

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