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

作　　者：Jan Vrbik 

机构地区：[1]Department of Mathematics and Statistics, Brock University, St. Catharines, Canada

出　　处：《Applied Mathematics》2019年第11期863-875,共13页应用数学（英文）

摘　　要：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.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.

关 键 词：SELF-NORMALIZED SUM CAUCHY Distribution Characteristic Functions FOURIER Transform Padé Approximation 

分 类 号：O17[理学—数学]