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.
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}
}