Accession Number : AD0631728

Title :   FOUR PROPERTIES OF TWO DIMENSIONAL RANDOM POINT PATTERNS.

Descriptive Note : Technical rept.,

Corporate Author : NORTHWESTERN UNIV EVANSTON IL DEPT OF GEOGRAPHY

Personal Author(s) : Dacey, Michael F.

Report Date : DEC 1965

Pagination or Media Count : 21

Abstract : Four properties of patterns formed by the random arrangement of points in a two dimensional region are stated. Part I gives order statistics for the areal uniform pattern which is defined by the probability law with distribution function F(x) = x(2), ) < x < 1. These order statistics are used in Part II to establish a relation for the moments of distance between points in a random arrangement of points in (i) the unit disk and (ii) the Euclidean plane. Part III compares (iii) the average distance between all pairs of points in a square array of m(2) points, and (iv) the expected distance between two points randomly placed in a square of the same dimensions. It is shown that the lattice distance approaches the measure of the square for even small values of m. Part IV obtains order distance for points in the Euclidean plane as a limiting result of order distance for n + l points randomly located in a square with unit area. (Author)

Descriptors :   (*GEOGRAPHY, PATTERN RECOGNITION), DISTRIBUTION, STOCHASTIC PROCESSES, MAPPING.

Subject Categories : Information Science
      Plasma Physics and Magnetohydrodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE