Abstract:
The Dirichlet distribution is a multivariate generalization of the Beta distribution. In this research, three methods of estimation for Dirichlet distribution which are maximum likelihood estimator (MLE), Method of Moment (MOM) and Quasi-likelihood estimator were used. This was done in other to obtain the most efficient method. An extensive simulation study was carried out on the basis of selected criterion (Bias, Variance, Mean absolute error and Mean square error) considering various sample sizes using R Version 3.42 win and R Studio 1.1.383 for the graphical and analytical procedures, the methods were also subjected to real life data. The performance of these methods were compared at different sample sizes it shows that the Quasi- likelihood estimator performs better in terms of Bias, than the other methods, while Method of Moment performs better in terms of Variance, than the other methods. Maximum likelihood estimator performs better in terms of Mean Absolute Error (MAE) and (MSE) than the other methods. The real life result shows that the Bayes factor of Dirichlet distribution give 57.95215, which implies a very strong evidence of the Goodness of fits, Quasi-likelihood estimator performs better among Method of Moment and Maximum likelihood.The Dirichlet distribution is efficient with higher precision and more adequacies in the estimate of the model, also the estimate of the model should be used in taking any prospective decision and can be reliable if large sample is involved.
