Abstract
Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. By using characteristic functions, we obtain several limit theorems extending previous results.
Highlights
The central limit theorem is one of the most remarkable results of the theory of probability 1, which is critical to understand inferential statistics and hypothesis testing 2, 3
More general measures of dependence are called mixing conditions, which are derived from the estimation of the difference between characteristic functions of averages of dependent and independent random variables
Our main interest in this note is the central limit theorem for dependent classes of random variables
Summary
Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. We obtain several limit theorems extending previous results
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