In this study, Dirichlet distribution, its history and usage areas are examined. Then, its characteristics are calculated and it is aimed to estimate parameters. To our knowledge, there is little research into parameter estimations that have been made for different sample sizes using the maximum likelihood method. To contribute to the literature, in the present study the maximum likelihood estimation, one of the most commonly used parameter estimation methods, was used. Newton-Raphson method and fixed-point iteration, which are numerical methods, were employed to estimate parameters. Then, software, which estimates parameters, was written using MATLAB.