FOUR PROPERTIES OF TWO DIMENSIONAL RANDOM POINT PATTERNS.
NORTHWESTERN UNIV EVANSTON IL DEPT OF GEOGRAPHY
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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 Fx x2, 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 m2 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
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