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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. Richardsonu0027s extrapolation is then applied to yield a corrected (second-order) approximation. Numerical results are presented to compare various approximations.

Corrected discrete approximations for the conditional and unconditional distributions of the continuous scan statistic