Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS
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4 novembre 2019: 1 événement

  • Planning des séminaires 2019-2020

    Lundi 4 novembre 11:00-12:00 - Aboubacar Yacouba Touré - LmB, Univ. Bourgogne Franche-Comté

    Séminaire PS : Asymptotic normality of the test statistics for the unified relative dispersion and relative variation indexes

    Résumé : Dispersion indexes with respect to the Poisson and binomial distributions are classical tools that are widely used to assess the conformity of the underlying distribution of an observed sample of count with one or the other of these theoretical distribution.
    Recently the exponential variation index have been proposed as an extension to positive continuous data. This paper aims to gather to study a unified definition of these indexes with respect to the relative variability of a non-negative natural exponential family of distributions through its variance function. We establish the strong consistency of the plug-in estimators of the indexes as well as their asymptotic normality. Since the exact distributions of the estimators are not available in closed form, we consider test of hypothesis relying on these estimators as test statistics with their asymptotic distributions. Simulation study suggests good behaviours of these test of hypothesis procedures, even for moderate sample sizes. Applicable examples are analyzed, including the lesser known references such negative binomial and inverse Gaussian, and improving the very usual case of the Poisson dispersion index. Concluding remarks are made with suggestions of possible extensions of this work.

    Lieu : Salle 316B - LmB

    En savoir plus : Planning des séminaires 2019-2020