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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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