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arXiv · 2104.06124

Confidence disc and square for Cauchy distributions

Yuichi Akaoka·Kazuki Okamura·Yoshiki Otobe
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Abstract

We will construct a confidence region of parameters for a sample of size $N$ from Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location parameter $\mu \in \mathbb{R}$ and a scale parameter $\sigma > 0$, we will infer them at once by regarding them as a single complex parameter $\gamma := \mu + i\sigma$. The region should be a domain in the complex plane, and we will give a simple and concrete formula to give the region as a disc and a square.

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Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe. 2021-04-13. Confidence disc and square for Cauchy distributions. https://doi.org/10.37863/umzh.v75i3.6797

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