On estimating dirichlet parameters—a comparison of initial values

Abstract

In many disciplines there is a need to model real world phenomena which occur as shares or as proportions. The Dirichlet distribution has been the predominant choice of researchers to model the proportions. The main advantage of using Dirichlet is its flexibility to accommodate a variety of shapes. The maximum likelihood approach has been the preferred route for estimating the Dirichlet parameters. Because this approach involves iterative procedures it is important to have good starting values. This study has identified at least three different methods in the literature for computing the initial estimates. Two are well known while the other has rarely been cited in the literature. This paper compares the different methods using a common simulated data set. The methods are compared with respect to speed of convergence, for different sample sizes. The paper also proposes two other simpler methods for the starting values. The results of this investigation indicate that one of the starting values proposed in this paper performs at least as well as the ones suggested in the literature Some questions for future work based on the results of this study are identified.

Keywords:

• Dirichlet distribution
• Maximum likelihood estimation
• Initial values
• Simulation