Mélange fini basé sur la distribution gamma et la distribution de Lindley généralisée

Abstract

In this thesis, we focus on the introduction of new probabilistic mo dels based on the strategy of mixing probability laws. First, we give a few reminders and basic notions of probability. Then, we present the formal definition of a general finite mixture model and propose two estimation methods for parameters : the maximum likelihood method and the expectation-maximization method. To familiarize ourselves with mixture models, we show a frequently used example. This is a mixture of Gaussian distributions. The variety of existing models in the literature makes it difficult to choose between them. For this reason, we present two classical criteria for determining the best model : the AIC criterion and the BIC criterion. In the fi nal chapter of this dissertation, we focus on finite mixing based on the generalized gamma-Lindley distribution, whether one- or two dimensional. In this context, we study various properties of these distributions, such as graphical representation, parameter estima tion, and so on.