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RANDOM PATHS ORIGINATING WITHIN A CONVEX REGION AND TERMINATING ON ITS SURFACE
Author(s) -
Enns E. G.,
Ehlers P. F.
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01154.x
Subject(s) - randomness , surface (topology) , regular polygon , normalization property , combinatorics , mathematics , euclidean space , convex body , space (punctuation) , euclidean geometry , geometry , convex hull , computer science , statistics , programming language , operating system
Summary A ray is defined as a straight line originating within an arbitrary convex body K in n ‐dimensional Euclidean space and terminating on the surface of K. The distributions of ray length are derived for three types of randomness. The results are expressed as functions of the overlap volume and overlap surface content of K with its translated self.