Caractérisations des familles exponentielles naturelles cubiques : étude des lois Beta généralisées et de certaines lois de Kummer

Abstract : This thesis has two different parts. In the first part we are interested in the real cubic natural exponential families such that their variance function is a polynomial of degree less than or equal to 3. We give three characterizations of such families using a Bayesian approach. One of these characterizations is based on a differential equation verified by the cumulant function. In a second part we study in depth the independence property of the type “Matsumoto-Yor” that was developed by Koudou and Vallois. This property involves the Kummer distribution of type 2 and the generalized beta ones. Using the conditioning and the rejection method, we give almost sure realization of these distributions. We characterize the family of Kummer distribution of type 2 with an algebraic equation involving the gamma ones. We proceed similarly with the generalized beta distributions
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Marwa Hamza. Caractérisations des familles exponentielles naturelles cubiques : étude des lois Beta généralisées et de certaines lois de Kummer. Mathématiques générales [math.GM]. Université de Lorraine, 2015. Français. ⟨NNT : 2015LORR0036⟩. ⟨tel-01751548⟩

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