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 μ ∈ ℝ and a scale parameter σ > 0 , we infer them simultaneously by regarding them as a single complex parameter γ : = μ + i σ . 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.