Confidence disc for Cauchy distributions

04/13/2021

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by   Yuichi Akaoka, et al.

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We will construct a confidence region of parameters for N samples from Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location parameter μ∈ℝ and a scale parameter σ > 0, we will infer them at once by regarding them as a single complex parameter γ := μ + i σ. Therefore 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.