The central limit theorem for sum-functions of m-tuples of spacings
Probability
2024-04-16 v1 Statistics Theory
Statistics Theory
Abstract
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior of the sum of functions of the m-tuples of successive spacings under the assumption that m can grow together with n. Asymptotic formulas for the expectation and variance of the sum and its asymptotic normality are established.
Cite
@article{arxiv.2404.09581,
title = {The central limit theorem for sum-functions of m-tuples of spacings},
author = {Sherzod M. Mirakhmedov},
journal= {arXiv preprint arXiv:2404.09581},
year = {2024}
}
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16 pages