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On a Mixture Model for Directional Data on the Sphere
Author(s) -
Franke Jürgen,
Redenbach Claudia,
Zhang Na
Publication year - 2016
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12169
Subject(s) - mathematics , gaussian , consistency (knowledge bases) , expectation–maximization algorithm , convergence (economics) , mixture model , focus (optics) , maximum likelihood , mathematical optimization , algorithm , statistical physics , statistics , geometry , physics , quantum mechanics , optics , economics , economic growth
We consider mixtures of general angular central Gaussian distributions as models for multimodal directional data. We prove consistency of the maximum‐likelihood estimates of model parameters and convergence of their numerical approximations based on an expectation–maximization algorithm. Then, we focus on mixtures of special angular central Gaussian distributions and discuss the details of a fast numerical algorithm, which allows to fit multimodal distributions to massive data, occurring, for example, in the study of the microstructure of materials. We illustrate the applicability with some data from fibre composites and from ceramic foams.