Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm |
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Authors: | Luca Bagnato Antonio Punzo |
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Affiliation: | 1. Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali, Università di Milano-Bicocca, Milan, Italy 2. Dipartimento di Economia e Impresa, Università di Catania, Catania, Italy
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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. |
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