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- Title
Finite mixtures of unimodal beta and gamma densities and the $$k$$-bumps algorithm.
- Authors
Bagnato, Luca; Punzo, Antonio
- Abstract
This paper addresses the problem of estimating a density, with either a compact support or a support bounded at only one end, exploiting a general and natural form of a finite mixture of distributions. Due to the importance of the concept of multimodality in the mixture framework, unimodal beta and gamma densities are used as mixture components, leading to a flexible modeling approach. Accordingly, a mode-based parameterization of the components is provided. A partitional clustering method, named $$k$$-bumps, is also proposed; it is used as an ad hoc initialization strategy in the EM algorithm to obtain the maximum likelihood estimation of the mixture parameters. The performance of the $$k$$-bumps algorithm as an initialization tool, in comparison to other common initialization strategies, is evaluated through some simulation experiments. Finally, two real applications are presented.
- Subjects
FINITE mixture models (Statistics); MAXIMUM likelihood statistics; CLUSTER analysis (Statistics); DISTRIBUTION (Probability theory); COMPUTER simulation; PARAMETER estimation; PROBLEM solving
- Publication
Computational Statistics, 2013, Vol 28, Issue 4, p1571
- ISSN
0943-4062
- Publication type
Article
- DOI
10.1007/s00180-012-0367-4