
Accession Number : AD0766804
Title : Intersections of Random Convex Regions.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS
Personal Author(s) : Dufour,Stuart W.
Report Date : 13 MAR 1973
Pagination or Media Count : 163
Abstract : By a random region is meant a region whose size and shape are fixed but whose orientation and location are random variables. The joint distribution of these random variables is assumed invariant under translations (but not necessarily under rotations) of the coordinate axes. Mean values are obtained describing the intersection of a random convex region with a fixed convex region, namely, the mean area and perimeter of the intersection of such regions on the plane and the mean volume and surface area of the intersection of such regions in three dimensions. These mean values are generalized to provide the mean area, volume, etc. of the intersection within a fixed convex region of n independent random convex regions which intersect the fixed region. Similar mean values, applicable to coverages problems, are obtained for the union within a fixed convex region of n independent random convex regions which intersect the fixed region. (Modified author abstract)
Descriptors : (*GEOMETRY, CONVEX SETS), (*CONVEX SETS, RANDOM VARIABLES), INTEGRALS, DISTRIBUTION FUNCTIONS, MEASURE THEORY, GRAPHICS, THEOREMS, PROBABILITY
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE