# Confidence disc and square for Cauchy distributions

• Y. Akaoka Department of Mathematics, Faculty of Science, Shinshu University, Nagano, Japan
• K. Okamura Department of Mathematics, Faculty of Science, Shizuoka University, Japan)
• Y. Otobe Department of Mathematics, Faculty of Science, Shinshu University, Nagano, Japan
Keywords: confidence disc, Cauchy distribution, central limit theorem

### Abstract

UDC 519.21

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

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Published
11.04.2023
How to Cite
Akaoka, Y., K. Okamura, and Y. Otobe. “Confidence Disc and Square for Cauchy Distributions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 3, Apr. 2023, pp. 305 -18, doi:10.37863/umzh.v75i3.6797.
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Section
Research articles