A higher order approximation to a percentage point of the distribution of a noncentral t-statistic without the normality assumption
A higher order approximation to a percentage point of the distribution of a noncentral t-statistic without the normality assumption
复制标题
无正态性假设的非中心 t 统计量分布百分比的高阶近似
DOI：
10.1080/03610918.2012.695841
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S
中科院分区：
文献类型：
--
作者：
Akahira;M.;Ohyauchi;N. and Kawai;S
非中心分布出现在两个样本问题中，并经常用于几个领域，例如生物统计学。Akahira给出了正态下非中心t分布的一个百分点的高阶近似，并且在数值上也优于其他近似。在本文中，没有正态性假设，我们以类似于Akahira的方式获得了非中心t统计量分布的一个百分点的高阶近似值，其中基于正态随机变量和chi统计量的线性组合的统计量起着重要作用。给出了该方法在非中心性参数置信限和置信区间中的应用。并将高阶近似与极限正态分布进行了数值比较，结果表明前者更为精确。数值计算的结果表明，高阶近似在实际情况下是有用的，当样本的大小不是很小。
Noncentral distributions appear in two sample problems and are often used in several fields, for example, in biostatistics. A higher order approximation for a percentage point of the noncentral t-distribution under normality is given by Akahira and is also shown to be numerically better than others. In this article, without the normality assumption, we obtain a higher order approximation to a percentage point of the distribution of a noncentral t-statistic, in a similar way to Akahira where the statistic based on a linear combination of a normal random variable and a chi-statistic takes an important role. Its application to the confidence limit and the confidence interval for a noncentrality parameter are also given. Further, a numerical comparison of the higher order approximation with the limiting normal distribution is done and the former one is shown to be more accurate. As a result of the numerical calculation, the higher order approximation seems to be useful in practical situations, when the size of sample is not so small.