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On the Distribution of the Bivariate Range

T. Cacoullos and H. DeCicco
Technometrics
Vol. 9, No. 3 (Aug., 1967), pp. 476-480
DOI: 10.2307/1266516
Stable URL: http://www.jstor.org/stable/1266516
Page Count: 5
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On the Distribution of the Bivariate Range
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Abstract

The distribution of the bivariate range R (defined below) is evidently unknown. This note discusses two approximations based on Monte Carlo moment data provided by the late S. S. Wilks. One approximation is based on an Edgeworth's series expansion and the other on a Chi-approximation. Upper bounds for the percentiles of R are discussed. Also given is a brief summary of other measures of dispersion of impact points randomly distributed on the plane of a target. Two such measures relating to the convex hull of the impact points are proposed.

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