Review on approximation approach for the distribution of the studentized mean

IF 3.6 1区 数学 Q1 MATHEMATICS, APPLIED
Menus Nkurunziza, L. Vermeire
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引用次数: 0

Abstract

In case of a normal population the studentized sample mean has the Student distribution with the sample size minus one as degrees of freedom. Simulation reports in the literature concluded that this distribution may be hold on as an acceptable approximation, and is often better than the classical normal approximation, in case of a general finite variance population provided moderate to large sample size. We provide a mathematical proof and add simulation evidence. A comparison of the performances of both approximations for the true distribution of the studentized statistic is given for the cumulative distribution function and for the quantile function, by asymptotic expansions and by simulations. A population condition such that the student approximation is universally better than the normal approximation is obtained.
学生化均值分布的近似方法综述
对于正态总体,学生化样本均值为样本容量为- 1的学生分布。文献中的模拟报告得出结论,这种分布可能是一个可接受的近似值,并且通常比经典的正态近似值更好,在一般有限方差总体提供中等到大样本量的情况下。给出了数学证明,并添加了仿真证据。通过渐近展开和模拟,比较了累积分布函数和分位数函数的两种近似对学习统计量真实分布的性能。得到了一个总体条件,使得学生近似普遍优于正态近似。
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来源期刊
CiteScore
6.30
自引率
17.10%
发文量
61
审稿时长
1 months
期刊介绍: The purpose of this journal is to provide a medium of exchange for scientists engaged in applied sciences (physics, mathematical physics, natural, and technological sciences) where there exists a non-trivial interplay between mathematics, mathematical modelling of real systems and mathematical and computer methods oriented towards the qualitative and quantitative analysis of real physical systems. The principal areas of interest of this journal are the following: 1.Mathematical modelling of systems in applied sciences; 2.Mathematical methods for the qualitative and quantitative analysis of models of mathematical physics and technological sciences; 3.Numerical and computer treatment of mathematical models or real systems. Special attention will be paid to the analysis of nonlinearities and stochastic aspects. Within the above limitation, scientists in all fields which employ mathematics are encouraged to submit research and review papers to the journal. Both theoretical and applied papers will be considered for publication. High quality, novelty of the content and potential for the applications to modern problems in applied sciences and technology will be the guidelines for the selection of papers to be published in the journal. This journal publishes only articles with original and innovative contents. Book reviews, announcements and tutorial articles will be featured occasionally.
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