The central limit theorem for sum-functions of m-tuples of spacings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929313927921664 |
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| author | Mirakhmedov, Sherzod M. |
| author_facet | Mirakhmedov, Sherzod M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The central limit theorem for sum-functions of m-tuples of spacings Mirakhmedov, Sherzod M. Probability Statistics Theory 60F10, 62G10, 62G20 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. |
| title | The central limit theorem for sum-functions of m-tuples of spacings |
| topic | Probability Statistics Theory 60F10, 62G10, 62G20 |
| url | https://arxiv.org/abs/2404.09581 |