2021•Open Journal of Mathematical SciencesOpen access
Rate of convergence in total variation for the generalized inverse Gaussian and the Kummer distributions
Institut Elie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine, Essomanda KONZOU, Laboratoire d’Analyse, de Modélisations Mathématiques et Applications, Université de Lomé, Lomé
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Abstract
The generalized inverse Gaussian distribution converges in law to the inverse gamma or the gamma distribution under certain conditions on the parameters. It is the same for the Kummer’s distribution to the gamma or beta distribution. We provide explicit upper bounds for the total variation distance between such generalized inverse Gaussian distribution and its gamma or inverse gamma limit laws, on the one hand, and between Kummer’s distribution and its gamma or beta limit laws on the other hand