Application of beta mixture distribution in data on GPA proportion and course scores at the MBTI Telkom University

Abstract

Cluster analysis is a multivariate analysis that aims to cluster objects or data so that objects or data that are in the same cluster have relatively more homogeneous properties than objects or data in different clusters. Probabilistic clustering method is often based on the assumption that data comes from a mixture of distributions, for examples Poisson, normal, lognormal, and Erlang. Thus the probabilistic clustering problem is transformed into a parameter estimation problem because the data is modeled by a cluster of mixture distribution. Data points that have the same distribution can be defined as one cluster. This distribution is applied to identify users on the community question answering site (CQA). In this paper the distribution of beta mixtures for single variable cases will be applied to the data on the proportion of student’s GPA in the subject of Business Statistics and Economic Mathematics of the Informatics Telecommunications Business Management, Faculty of Economics and Business, Telkom University. Based on the results of the analysis on the GPA data, Economic Mathematics and  Business Statistics shows the smallest integrated classification likelihood estimation Bayesian criterion (ICL BIC) scores in two clusters for GPA and Business Statistics Value. While the ICL value of BIC in Economic Mathematics shows the smallest ICL BIC value in one cluster. Then it can be concluded that GPA and Business Statistics occur in Mixture 2 clusters.