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

Luca Bagnato, Antonio Punzo

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1571-1597
Number of pages27
JournalComputational Statistics
Publication statusPublished - 2013


  • Bump algorithm
  • EM algorithm
  • Finite mixtures of densities


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