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Place probabilities in normal order statistics models for horse races

Published online by Cambridge University Press:  14 July 2016

R. J. Henery
R. J. Henery*
Affiliation:
University of Strathclyde
*
∗Postal address: Department of Mathematics, Livingstone Tower, 26 Richmond St, Glasgow G1 1XH, U.K.
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Abstract

Independent observations X0, X1…, XN+1 are drawn from each of N populations whose distribution functions F(x – θi) have means θ i, 0 ≦ i < N, and we wish to calculate the probability Pk;N that X0 is the k th largest observation. For normal populations an approximation is given for PK;N based on a Taylor series expansion in the θ 's. If F(x) has an increasing failure rate, as is the case for the normal, an upper bound can be given for the ‘win' probability P1;N Some moment relations for normal order statistics are also given.

Keywords

PLACE PROBABILITYORDER STATISTICSNORMALSYMMETRIC FUNCTIONSUPPER BOUNDMOMENT RELATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 839 - 852
Copyright
Copyright © Applied Probability Trust 1981 

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References

Brook, D. and Upton, G. J. G. (1974) Biases in local government elections due to position on the ballot paper. Appl. Statist. 23, 414–419.CrossRefGoogle Scholar
David, H. A. (1970) Order Statistics. Wiley, New York.Google Scholar
Henery, R. J. (1981) Permutation probabilities as models for horse races. J. R. Statist. Soc. B 43, 86–91.Google Scholar
Kendall, M. G. and Stuart, A. (1969) The Advanced Theory of Statistics , Vol. I, Cambridge University Press.Google Scholar
Plackett, R. L. (1975) The analysis of permutations. Appl. Statist. 23, 193–202.CrossRefGoogle Scholar
Ruben, H. (1954) On the moments of order statistics in samples from normal populations. Biometrika 41, 200–227.CrossRefGoogle Scholar
Ruben, H. (1960) On the geometrical moments of skew-regular simplices in hyperspherical space with some applications in geometry and mathematical statistics. Acta Math. 103, 1–23.CrossRefGoogle Scholar