English

Corrected Discrete Approximations for the Conditional and Unconditional Distributions of the Continuous Scan Statistic

Probability 2016-02-09 v1

Abstract

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete approximation). With the help of a change-of-measure argument, we derive the first-order term of the discrete approximation which involves some functionals of the Poisson process. Richardson's extrapolation is then applied to yield a corrected (second-order) approximation. Numerical results are presented to compare various approximations.

Keywords

Cite

@article{arxiv.1602.02597,
  title  = {Corrected Discrete Approximations for the Conditional and Unconditional Distributions of the Continuous Scan Statistic},
  author = {Yi-Ching Yao and Daniel Wei-Chung Miao and Xenos Chang-Shuo Lin},
  journal= {arXiv preprint arXiv:1602.02597},
  year   = {2016}
}

Comments

22 pages

R2 v1 2026-06-22T12:45:30.011Z