(1) Institute of Statistics, Texas A & M University, 77843 College Station, Texas, USA;(2) Battelle Northwest Laboratories, P.O. Box 999, 99352 Richland, Washington, USA;(3) Institute of Statistics, Texas A & M University, USA
Abstract:
The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.