In this paper the Lorenz curve proposed by Abdalla and Hassan is fitted to grouped income data of Abu-Dhabi Emirate family expenditure survey, 1997, using Maximum likelihood estimation method and assuming that income shares follow a Dirichlet distribution. Employing Abdalla and Hassan's together with some known parametric Lorenz models, estimates based on the maximum likelihood are compared with those based on non-linear least squares techniques. Given the nature of the distribution of income and the distinct characteristics of Abu-Dhabi Emirate, it is evident that the maximum likelihood estimation approach produces comparable parameter estimates to the non-linear least squares techniques, but higher standard errors and less goodness of fit. Under the two estimation techniques, the model proposed by Abdalla and Hassan performed well better than some well known parametric models in the literature.