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 · Journal of Applied Probability · 2017
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). Using 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.