Estimation for the Distribution of Two-dimensional Discrete Scan Statistics

This paper concerns the application of the method introduced in (Haiman, Extremes, 3:349–361, 2000) to estimate the distribution of two-dimensional discrete scan statistics. This method makes it possible to establish sharp bounds for the estimation errors. The method involves the estimation by simulation of the distribution of scan statistics for the particular rectangle sets of size 2×2, 2×3, 3×3, where the unit is the (m ₁×m ₂) dimension of the rectangular scanning window, m ₁, m ₂ ∈ℕ. We perform several numerical applications and compare our results with results obtained by other authors.