The REBMIX Algorithm and the Univariate Finite Mixture Estimation

Abstract

The REBMIX algorithm is presented and applied to estimation of finite univariate mixture densities. The algorithm identifies the component parameters, mixing weights, and number of the components successively. Significant improvement is achieved by replacing the rigid restraints with the loose ones, which enables improved modelling of overlapped components. The algorithm is controlled by the extreme relative deviations, total of positive relative deviations, and information criteria. It enables also the modeling of multivariate finite mixtures. However, the article considers univariate normal, lognormal, and Weibull finite mixtures solely. The REBMIX software is available on http://www.fs.uni-lj.si/lavek.

Keywords:

• Finite mixtures
• Lognormal distribution
• Normal distribution
• Parameter estimation
• Weibull distribution

Mathematics Subject Classification:

• Primary 62
• Secondary F10