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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
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Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Caractérisations des familles exponentielles naturelles cubiques : étude des lois Beta généralisées et de certaines lois de Kummer / Characterizations of the cubic natural exponential families : Study of generalized beta distributions and some Kummer’s distributionsHamza, Marwa 18 May 2015 (has links)
Cette thèse contient deux parties différentes. Dans la première partie, nous nous sommes intéressés aux familles exponentielles naturelles cubiques dont la fonction variance est un polynôme de degré inférieur ou égal à 3. Nous donnons trois caractérisations de ces familles en se basant sur une approche Bayesienne. L’une de ces caractérisations repose sur le fait que la fonction cumulante vérifie une équation différentielle. La deuxième partie de notre travail est consacrée aux conséquences de la propriété d’indépendance de type « Matsumoto-Yor » qui a été développée par Koudou et Vallois. Cette propriété fait intervenir la famille de lois de Kummer de type 2 et les lois Beta généralisées. En se basant sur la méthode de conditionnement et sur la méthode de rejet, nous donnons des réalisations presque sûre de ces distributions de probabilités. D’autre part, nous caractérisons la famille de lois de Kummer de type 2 (resp. les lois Beta généralisées) par une équation algébrique impliquant des lois gamma (resp. les lois Beta) / 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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Developing new methods for estimating population divergence times from sequence dataSvärd, Karl January 2021 (has links)
Methods for estimating past demographic events of populations are powerful tools in order to get insights of otherwise hidden pasts. The genetic data of people is a valuable resource for these purposes as patterns of variation can inform of the past evolutionary forces and historical events that generated them. There is, however, a lack of methods within the field that uses this information to its full extent. That is why this project has looked at developing a set of new alternatives for estimating demographic events. The work done has been based on modifying the purely sequence based method TTo (Two-Two-outgroup) for estimating divergence times of two populations. The modifications consisted of using beta distributions to model the polymorphic diversity of the ancestral population in order to increase the max sample size possible. The finished project resulted in two implemented methods: TT-beta and a partial variant of MM. TT-beta was able to produce estimations in the same region as TTo and showed that the usage of beta distributions had real potential. For MM there only was a partial implementation able to be done, but this one also showed promise and the ability to use varying sample sizes to estimate demographic values.
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