Corrected Discrete Approximations for the Conditional and Unconditional   Distributions of the Continuous Scan Statistic
  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. 
Yi-Ching Yao, Daniel Wei-Chung Miao, Xenos Chang-Shuo Lin
math.PR