Mixtures of Multivariate Power Exponential Distributions

Biometrics. 2015 Dec;71(4):1081-9. doi: 10.1111/biom.12351. Epub 2015 Jul 1.


An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness have received much attention in the model-based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail-weight and peakedness of data. A family of parsimonious models is proposed using an eigen-decomposition of the scale matrix. A generalized expectation-maximization algorithm is presented that combines convex optimization via a minorization-maximization approach and optimization based on accelerated line search algorithms on the Stiefel manifold. Lastly, the utility of this family of models is illustrated using both toy and benchmark data.

Keywords: GEM-algorithm; Mixture models; Model-based clustering; Multivariate power exponential; Stiefel manifold.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Animals
  • Bayes Theorem
  • Biometry / methods*
  • Cluster Analysis
  • Computer Simulation
  • Databases, Factual / statistics & numerical data
  • Female
  • Humans
  • Likelihood Functions
  • Male
  • Models, Statistical*
  • Multivariate Analysis*
  • Normal Distribution
  • Statistical Distributions