We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The multivariate leptokurtic-normal distribution and its application in model-based clustering.
- Authors
Bagnato, Luca; Punzo, Antonio; Zoia, Maria G.
- Abstract
This article proposes the elliptical multivariate leptokurtic-normal (MLN) distribution to fit data with excess kurtosis. The MLN distribution is a multivariate Gram-Charlier expansion of the multivariate normal (MN) distribution and has a closed-form representation characterized by one additional parameter denoting the excess kurtosis. It is obtained from the elliptical representation of the MN distribution, by reshaping its generating variate with the associated orthogonal polynomials. The strength of this approach for obtaining the MLN distribution lies in its general applicability as it can be applied to any multivariate elliptical law to get a suitable distribution to fit data. Maximum likelihood is discussed as a parameter estimation technique for the MLN distribution. Mixtures of MLN distributions are also proposed for robust model-based clustering. An EM algorithm is presented to obtain estimates of the mixture parameters. Benchmark real data are used to show the usefulness of mixtures of MLN distributions. The Canadian Journal of Statistics 45: 95-119; 2017 © 2016 Statistical Society of Canada
- Subjects
KURTOSIS; MIMICRY (Biology); MULTIVARIATE analysis; UNIVARIATE analysis; STATISTICS
- Publication
Canadian Journal of Statistics, 2017, Vol 45, Issue 1, p95
- ISSN
0319-5724
- Publication type
Article
- DOI
10.1002/cjs.11308