This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal distribution, we introduce a data augmentation approach using the Gibbs sampler, where intermediate values are treated as missing values and samples from a truncated normal distribution conditional on the observed sample mean, minimum, and maximum values. Through simulation studies, we demonstrate that our method achieves estimation accuracy comparable to theoretical expectations.

翻译：本文提出了一种贝叶斯方法，用于在仅能获取有限汇总统计量（样本均值、最小值、最大值及样本量）时估计正态分布的参数。为估计正态分布参数，我们引入了一种采用吉布斯采样器的数据增强方法，其中将中间值视为缺失值，并在给定观测到的样本均值、最小值及最大值的条件下从截断正态分布中采样。通过模拟研究，我们证明该方法能达到与理论预期相当的估计精度。