Author(s)

Jan Vrbik

Department of Mathematics and Statistics, Brock University, St. Catharines, Canada.

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.

Self-Normalized Sum, Cauchy Distribution, Characteristic Functions, Fourier Transform, Padé Approximation

Vrbik, J. (2019) A Note on “Limit Distributions of Self-Normalized Sums” Using Cauchy-Generated Samples. Applied Mathematics, 10, 863-875. doi: 10.4236/am.2019.1011062.