Metrika

, Volume 27, Issue 1, pp 145–151 | Cite as

On the distribution of a distance function on the sphere

  • M. Yaqub
  • A. H. Khan
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Summary

The distribution of the square of the distance between a random point and a fixed point on ap-dimensional unit sphere when (i) the two points lie on the whole sphere and (ii) the two points lie in the positive quadrant, has been derived, assuming that the random point is distributed proportionally to exp (ky1), wherek is a concentration parameter. Then-th order moment in both cases is also obtained.

Keywords

Distance Function Unit Sphere Random Point Order Moment Concentration Parameter 

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References

  1. Erdelyi, A., et al.: Tables of integral transforms. Vol. I. New York 1954.Google Scholar
  2. Khan, A.H., andM. Yaqub: On a distribution of a distance function. Bull. Internal. Statist. Inst.47, 1977, 280–283 (Proc. of 41st Session of ISI).Google Scholar
  3. Mardia, K.V.: Statistics of Directional Data. New York 1972.Google Scholar
  4. Matusita, K.: Decision rules based on distance for problem of fit, two samples and estimation. Ann. Math. Statist.26, 1955, 631–640.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Physica-Verlag 1980

Authors and Affiliations

  • M. Yaqub
    • 1
  • A. H. Khan
    • 1
  1. 1.Department of StatisticsAligarh Muslim UniversityAligarhIndia

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