Nowadays, a great number of positive data has been occurred naturally in many applications, however, it was not adequately analyzed. In this article, we propose a novel statistical approach for clustering multivariate positive data. Our approach is based on a finite mixture model of inverted Beta-Liouville (IBL) distributions, which is proper choice for modeling and analysis of positive vector data. We develop two different approaches to learn the proposed mixture model. Firstly, the maximum likelihood (ML) is utilized to estimate parameters of the finite inverted Beta-Liouville mixture model in which the right number of mixture components is determined according to the minimum message length (MML) criterion. Secondly, the variational Bayes (VB) is adopted to learn our model where the parameters and the number of mixture components can be determined simultaneously in a unified framework, without the requirement of using information criteria. We investigate the effectiveness of our model by conducting a series of experiments on both synthetic and real data sets
