Touré Aboubacar Y, Dossou-Gbété Simplice, Kokonendji Célestin C
Laboratoire de Mathématiques de Besançon UMR 6623 CNRS-UFC, Université Bourgogne Franche-Comté, Besançon cedex, France.
Laboratoire de Mathématiques et de leurs Applications de Pau, Université de Pau et des Pays de l'Adour, Pau cedex, France.
J Appl Stat. 2020 Jun 14;47(13-15):2479-2491. doi: 10.1080/02664763.2020.1779193. eCollection 2020.
Dispersion indexes with respect to the Poisson and binomial distributions are widely used to assess the conformity of the underlying distribution from an observed sample of the count with one or the other of these theoretical distributions. Recently, the exponential variation index has been proposed as an extension to nonnegative continuous data. This paper aims to gather to study the unified definition of these indexes with respect to the relative variability of a nonnegative 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 normalities. Since the exact distributions of the estimators are not available in closed form, we consider the test of hypothesis relying on these estimators as test statistics with their asymptotic distributions. Simulation studies globally suggest good behaviours of these tests of hypothesis procedures. Applicable examples are analysed, including the lesser-known references such as 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.
关于泊松分布和二项分布的离散度指标被广泛用于根据计数的观测样本评估基础分布与这些理论分布之一的符合程度。最近，指数变异指标已被提出作为对非负连续数据的一种扩展。本文旨在通过其方差函数来研究这些指标关于非负自然指数族分布的相对变异性的统一定义。我们建立了这些指标的插件估计量的强一致性及其渐近正态性。由于估计量的精确分布没有封闭形式，我们考虑以这些估计量作为检验统计量并依据其渐近分布的假设检验。模拟研究总体上表明这些假设检验程序表现良好。分析了适用的例子，包括负二项分布和逆高斯分布等不太知名的分布，并改进了泊松离散度指标这种非常常见的情况。最后给出了结论性评论以及可能扩展的建议。
