Spacing Methods and Their Applications to Scan Statistics

The scan statistics can be used in many areas of science to test for uniformity. In this chapter a review of spacing methods on scan statistic for the continuous conditional case is presented. This method is based on repeated use of a basic recursion to break up the joint distribution of linear combinations of spacings into simpler components which are easily evaluated. The final answers produced by this approach are piecewise polynomials whose coefficients are computed exactly. These expressions can be stored and later used to rapidly compute numerical answers which are accurate to any required degree of precision.