Confidence disc and square for Cauchy distributions - Akaoka, Y.; Okamura, K.; Otobe, Y. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 519.21We 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 $μ \in\mathbb{R}$ and a scale parameter $σ > 0,$ we infer them simultaneously by regarding them as a single complex parameter $γ := μ + iσ.$ 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.