Abstract
Two independent random sets are formed by finite systems of independent random variables uniformly distributed on the unit circle. A formula for the distribution of the distance between the sets is derived.
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REFERENCES
S. Karlin, A First Course in Stochastic Processes, Academic Press, New York, 1968.
Yu. V. Prokhorov and Yu. A. Rozanov, Probability Theory [in Russian], Nauka, Moscow, 1987.
B. Silverman and T. Brown, "Short distances, flat triangles, and Poisson limits," J. Appl. Probab., 15 (1978), no. 4, 816-826.
T. Brown and B. Silverman, "Rates of Poisson convergence for U-statistics," J. Appl. Probab., 16 (1979), no. 2, 428-432.
A. Barbour and G. Eagleson, "Poisson convergence for dissociated statistics," J. Royal Statistics Soc. Ser. B, 46 (1984), no. 3, 397-401.
A. A. Grusho, "On the distributions of U-statistics" Teor. Veroyatnost. i Primenen. [Theory Probab. Appl.], 32 (1987), no. 2, 400-404.
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Uglanov, A.V. Calculation of the Distance betweeen Two Random Sets. Mathematical Notes 72, 841–846 (2002). https://doi.org/10.1023/A:1021446130926
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DOI: https://doi.org/10.1023/A:1021446130926