English

Bayesian Parameter Estimation of Normal Distribution from Sample Mean and Extreme Values

Methodology 2024-11-21 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2411.13131,
  title  = {Bayesian Parameter Estimation of Normal Distribution from Sample Mean and Extreme Values},
  author = {Tomoki Matsumoto},
  journal= {arXiv preprint arXiv:2411.13131},
  year   = {2024}
}
R2 v1 2026-06-28T20:06:01.196Z