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.

Bagnato, L., Punzo, A., Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm, <<COMPUTATIONAL STATISTICS>>, 2013; 28 (4): 1571-1597. [doi:10.1007/s00180-012-0367-4] [http://hdl.handle.net/10807/40383]

Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm

Bagnato, Luca;
2013

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.
2013
Inglese
Bagnato, L., Punzo, A., Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm, <<COMPUTATIONAL STATISTICS>>, 2013; 28 (4): 1571-1597. [doi:10.1007/s00180-012-0367-4] [http://hdl.handle.net/10807/40383]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/40383
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