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On random simplices in product distributions

Published online by Cambridge University Press:  14 July 2016

Hiroshi Maehara
Hiroshi Maehara*
Affiliation:
Ryukyu University
*
∗Postal address: Department of Mathematics, Ryukyu University, Naha, Okinawa, Japan.
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Abstract

It is proved that the r-dimensional volume Vn of the r-simplex spanned by r + 1 sample points taken from the n-fold product distribution of a distribution F is asymptotically normal as n →∞.

Keywords

RANDOM SIMPLEXPRODUCT DISTRIBUTIONASYMPTOTIC NORMALITY OF VOLUME
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 553 - 558
Copyright
Copyright © Applied Probability Trust 1980 

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References

Kendall, M. G. and Stuart, A. S. (1969) The Advanced Theory of Statistics, Vol. I. Griffin, London.Google Scholar
Rao, C. R. (1973) Linear Statistical Inference and Its Applications, 2nd ed. Wiley, London.CrossRefGoogle Scholar
Ruben, H. (1977) The volume of a random simplex in an n-ball is asymptotically normal. J. Appl. Prob. 14, 647–653.Google Scholar