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On the distribution of a distance function on the sphere

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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 (ky 1), wherek is a concentration parameter. Then-th order moment in both cases is also obtained.

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References

  • Erdelyi, A., et al.: Tables of integral transforms. Vol. I. New York 1954.

  • 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).

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  • Mardia, K.V.: Statistics of Directional Data. New York 1972.

  • Matusita, K.: Decision rules based on distance for problem of fit, two samples and estimation. Ann. Math. Statist.26, 1955, 631–640.

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Authors and Affiliations

  1. Department of Statistics, Aligarh Muslim University, 202001, Aligarh, India

    M. Yaqub & A. H. Khan

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  1. M. Yaqub
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  2. A. H. Khan
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Yaqub, M., Khan, A.H. On the distribution of a distance function on the sphere. Metrika 27, 145–151 (1980). https://doi.org/10.1007/BF01893591

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  • DOI: https://doi.org/10.1007/BF01893591

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