A Note on “Limit Distributions of Self-Normalized Sums” Using Cauchy-Generated Samples

Abstract

In this case study, we would like to illustrate the utility of characteristic functions, using an example of a sample statistic defined for samples from Cauchy distribution. The derivation of the corresponding asymptotic probability density function is based on [1], elaborating and expanding the individual steps of their presentation, and including a small extension; our reason for such a plagiarism is to make the technique, its mathematical tools and ingenious arguments available to the widest possible audience.