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Distances on circles, toruses and spheres

Published online by Cambridge University Press:  14 July 2016

B. W. Silverman
B. W. Silverman*
Affiliation:
University of Cambridge
*
*Now at the University of Oxford.
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Abstract

Families of heavily dissociated random variables are defined and discussed. These include families of the form g(Yi, Yj) for some suitable function g of two arguments and independent uniformly distributed random variables Y1, Y2, ··· on the circle, the torus or the sphere. The weak convergence of the empirical distribution process is discussed. The particular case of distances between pairs of observations on the circle is considered in greater detail.

Keywords

DISSOCIATED RANDOM VARIABLESDIRECTIONAL DATAEMPIRICAL DISTRIBUTION FUNCTIONTEST OF UNIFORMITYTEST OF RANDOMNESSTEST OF CLUSTERINGKOLMOGOROV-SMIRNOV
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 136 - 143
Copyright
Copyright © Applied Probability Trust 1978 

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References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
McGinley, W. G. and Sibson, R. (1975) Dissociated random variables. Math. Proc. Camb. Phil. Soc. 77, 185–188.CrossRefGoogle Scholar
Mardia, K. V. (1972) Statistics of Directional Data. Academic Press, New York.Google Scholar
Ripley, B. D. (1976) The second-order analysis of stationary point processes. J. Appl. Prob. 13, 255–266.CrossRefGoogle Scholar
Siegel, S. (1956) Nonparametric Statistics for the Behavioural Sciences. McGraw-Hill, New York.Google Scholar
Silverman, B. W. (1976) Limit theorems for dissociated random variables. Adv. Appl. Prob. 8, 806–819.CrossRefGoogle Scholar