Confidence disc and square for Cauchy distributions - Akaoka, Y.; Okamura, K.; Otobe, Y. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
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 μ 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.