基于置信分布的多个对数正态总体的公共均值的置信区间的构建（英文）

Confidence Intervals for the Common Mean of Several Log-normal Populations Using Confidence Distributions

在实际应用中需要拟合正的偏态数据时,对数正态分布是通常的选择.当通过多重比较确定了多个对数正态分布总体的均值相同时,如何能够利用更多的信息,同时使用这些对数正态分布总体的信息来构建公共均值的置信区间成为了众多学者颇为关注的问题.本篇文章提出了一种新的基于置信分布的方法来构建多个对数正态总体公共均值的置信区间,该方法通过对相关量的样本方差进行加权来提高效率.进而对文中提出的基于置信分布的置信区间的构建方法进行了蒙特卡洛模拟研究,模拟结果表明,我们提出的构建方法可以得到很好的覆盖概率和较短的区间宽度.文章的最后用三个实际数据来验证了文中所提出方法的表现.

The log-normal distribution is a common choice for modeling positively skewed data arising from many practical applications.This article introduces a new method of constructing confidence interval for a common mean shared by several log-normal populations through confidence distributions,which combines all information from independent sources.We develop a non-trivial weighting approach by taking account of the sample variances of related quantities to enhance efficiency.Combined confidence distributions are used to construct confidence intervals for the common mean and a simplified version of one existing method is also proposed.We conduct simulation studies to evaluate the performance of the proposed methods in comparison with existing methods.Our simulation results show that the weighting approach yields shorter interval length than the non-weighting approach.The newly proposed confidence intervals perform very well in terms of empirical coverage probability and average interval length.Finally,applications of the proposed methodology is illustrated through three real data examples.