Confidence disc and square for Cauchy distributions
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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