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arXiv · 1602.02597

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

Yi-Ching Yao·Daniel Wei-Chung Miao·Xenos Chang-Shuo Lin
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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.

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Yi-Ching Yao, Daniel Wei-Chung Miao, Xenos Chang-Shuo Lin. 2016-02-08. Corrected Discrete Approximations for the Conditional and Unconditional Distributions of the Continuous Scan Statistic. https://arxiv.org/abs/1602.02597

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