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This paper is concerned with a class of exponential dispersion distributions. We particularly focused on the mixture models, which represent an extension of the Gaussian distribution. It should be noted that the parameters estimation of mixture distributions is an important task in statistical processing. In order to estimate the parameters vector, we proposed a formulation of the Expectation-Maximization algorithm (EM) under exponential dispersion mixture distributions. Also, we developed a hybrid algorithm called Expectation-Maximization and Method of moments algorithm (EMM). Under mild regularity, several convergence results of the EMM algorithm were obtained. Through simulation studies, the robustness of the EMM was proved and the strong consistency of the EMM sequence appeared when the data set size and the number of iterations tend to infinity.