Bayesian Parameter Estimation of Normal Distribution from Sample Mean and Extreme Values
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913581818183680 |
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| author | Matsumoto, Tomoki |
| author_facet | Matsumoto, Tomoki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian Parameter Estimation of Normal Distribution from Sample Mean and Extreme Values Matsumoto, Tomoki Methodology 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. |
| title | Bayesian Parameter Estimation of Normal Distribution from Sample Mean and Extreme Values |
| topic | Methodology |
| url | https://arxiv.org/abs/2411.13131 |