标题： 基于变换样本均值的一参数分布的准确推断 显示英文标题

标题： Accurate inference for a one parameter distribution based on the mean of a transformed sample

摘要： 统计学中的大量推断是基于将一个统计量近似为正态分布的假设。 这样做产生的误差通常为$O(n^{-1/2})$，当分布严重偏斜或偏倚时，误差可能非常大。 本说明展示了如何将此误差减少到$O(n^{-(j+1)/2})$，其中$j$是一个给定的整数。 所考虑的情况是，统计量是来自连续单参数分布的样本值的均值，在样本经过初始变换之后。 显示英文摘要

摘要： A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or skew. This note shows how one may reduce this error to $O(n^{-(j+1)/2})$, where $j$ is a given integer. The case considered is when the statistic is the mean of the sample values from a continuous one-parameter distribution, after the sample has undergone an initial transformation.