多个对数正态总体共同均值的估计问题研究

Research on the Estimation of Common Mean for Multiple Log-Normal Populations

摘要: 若随机变量 X=lnY～N(µ，σ²), 则随机变量 X 服从对数正态分布，对数正态分布用来表示一类正右偏数据，实际应用非常广泛[1]。在很多情况下，数据的来源有不同的背景，对于单个总体的研究[2]已经不能满足我们的需求，此时的主要目的是基于几个总体来研究他们的共同参数问题。本文对于单个样本利用广义推断的方法给出均值[3]广义枢轴量，然后基于每个总体所抽取的样本量和近似样本方差的广义枢轴量给出不同总体共同均值的广义枢轴量的加权平均，得到共同均值的广义置信区间，利用R语言进行数值模拟，得到的覆盖概率接近置信水平。

Abstract: If the random variable  X=lnY～N(µ，σ²) , then the random variable X follows the log-normal distribution, which is used to describe a class of positive right-skewed data and the practical ap-plication is very extensive [1]. In many cases, the source of data has different backgrounds, for a single population research [2] has been unable to meet our needs, so the main purpose of this time is to study their common parameters based on several populations. In this paper, the generalized pivot of the mean [3] is given for a single sample by means of generalized inference, and then the weighted average of the generalized pivot is given for different populations of common mean based on the sample size extracted from each population and the generalized pivot of approximate sample variance. Then the generalized confidence interval of the common mean is obtained. The probability of coverage is close to the confidence level using R.