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

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  • Luca Bagnato
  • Antonio Punzo

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. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Luca Bagnato & Antonio Punzo, 2013. "Finite mixtures of unimodal beta and gamma densities and the $$k$$ -bumps algorithm," Computational Statistics, Springer, vol. 28(4), pages 1571-1597, August.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:4:p:1571-1597
    DOI: 10.1007/s00180-012-0367-4
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