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On the Distribution of the Bivariate Range
T. Cacoullos and H. DeCicco
Vol. 9, No. 3 (Aug., 1967), pp. 476-480
Published by: Taylor & Francis, Ltd. on behalf of American Statistical Association and American Society for Quality
Stable URL: http://www.jstor.org/stable/1266516
Page Count: 5
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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.
Technometrics © 1967 American Statistical Association