TY - JOUR

T1 - Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm

AU - Bagnato, Luca

AU - Punzo, Antonio

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Bump algorithm

KW - EM algorithm

KW - Finite mixtures of densities

KW - Bump algorithm

KW - EM algorithm

KW - Finite mixtures of densities

UR - http://hdl.handle.net/10807/40383

UR - http://link.springer.com/article/10.1007%2fs00180-012-0367-4?li=true

U2 - 10.1007/s00180-012-0367-4

DO - 10.1007/s00180-012-0367-4

M3 - Article

SN - 0943-4062

VL - 28

SP - 1571

EP - 1597

JO - Computational Statistics

JF - Computational Statistics

ER -