Practical properties of the CUSUM process
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910824873852928 |
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| author | Baron, Michael Malov, Sergey V. |
| author_facet | Baron, Michael Malov, Sergey V. |
| contents | We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing algorithms, lower and upper bounds, as well as asymptotes. Results are applied to single, multiple, and transient change-point problems, for the calculation of thresholds that provide a desired control of familywise false alarm rates, as well as the quantiles of queuing processes and probabilities of their large deviation at least once over a given time interval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Practical properties of the CUSUM process Baron, Michael Malov, Sergey V. Probability Statistics Theory 60G50, 62E20, 60F10, 60G46, 60K25 We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing algorithms, lower and upper bounds, as well as asymptotes. Results are applied to single, multiple, and transient change-point problems, for the calculation of thresholds that provide a desired control of familywise false alarm rates, as well as the quantiles of queuing processes and probabilities of their large deviation at least once over a given time interval. |
| title | Practical properties of the CUSUM process |
| topic | Probability Statistics Theory 60G50, 62E20, 60F10, 60G46, 60K25 |
| url | https://arxiv.org/abs/2502.09185 |