TITLE:
A Note on “Limit Distributions of Self-Normalized Sums” Using Cauchy-Generated Samples
AUTHORS:
Jan Vrbik
KEYWORDS:
Self-Normalized Sum, Cauchy Distribution, Characteristic Functions, Fourier Transform, Padé Approximation
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.11,
October
25,
2019
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.