An Accurate Approximation for Distance Distributions Arising in Airtanker Positioning and Related Problems

摘要

A moment-based methodology is proposed for approximating the distribution of the distance between two random points belonging to sets that are composed of convex polygons. The resulting density approximants are expressed as the product of a beta density function and a polynomial adjustment. Because points and line segments are merely polygons projected to lower dimensions, the method can readily be used to determine the distribution of the distance between a fixed point or a line segment and polygons. In this way, it is possible to determine the distribution of the distance from an airtanker base to an initial attack zone, represented by either a convex polygon or line segment. Several illustrative examples as well as applications to the distance between an airtanker's base and its initial attack zone, and between a transportation corridor and a wildland-urban interface are presented. [PUBLICATION ABSTRACT]