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A simulation study of random caps on a sphere

Published online by Cambridge University Press:  24 August 2016

H. Solomon  and
C. Sutton
H. Solomon*
Affiliation:
Stanford University
C. Sutton*
Affiliation:
Stanford University
*
∗Postal address: Department of Statistics, Sequoia Hall, Stanford, CA 94305, USA.
∗Postal address: Department of Statistics, Sequoia Hall, Stanford, CA 94305, USA.
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Abstract

This paper describes the computer simulation of a coverage problem in geometric probability, that of placing random caps on the surface of a sphere. The simulation results were compared with exact values, where known, and the differences were negligible. This suggested the use of simulation results to assess several approximation formulas in the literature.

Keywords

RANDOM SPHERICAL CAPSGEOMETRICAL PROBABILITY
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 951 - 960
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This paper was prepared with the partial support of the Office of Naval Research under Contract N00014–76-C-0475.

References

Gilbert, E. N. (1965) The probability of covering a sphere with N circular caps. Biometrika 52, 323–330.CrossRefGoogle Scholar
Miles, R. E. (1969) The asymptotic values of certain coverage probabilities. Biometrika 56, 661–680.CrossRefGoogle Scholar
Moran, P. A. P. and Fazekas De St. Groth, S. (1962) Random circles on a sphere. Biometrika 49, 389–396.CrossRefGoogle Scholar
Solomon, H. (1978) Geometric Probability. CBMS-NSF Regional Conference Series in Applied Mathematics, No. 28. SIAM, Philadelphia, Pa. CrossRefGoogle Scholar
Wendel, J. G. (1962) A problem in geometric probability. Math. Scand. 11, 109–111.CrossRefGoogle Scholar