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.
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