Place probabilities in normal order statistics models for horse races
- 1 September 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 18 (04) , 839-852
- https://doi.org/10.1017/s0021900200034197
Abstract
Independent observations X 0, X 1…, X N+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 P k;N that X 0 is the k th largest observation. For normal populations an approximation is given for P K;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 P 1;N Some moment relations for normal order statistics are also given.Keywords
This publication has 3 references indexed in Scilit:
- Biases in Local Government Elections Due to Position on the Ballot PaperJournal of the Royal Statistical Society Series C: Applied Statistics, 1974
- On the geometrical moments of skew-regular simplices in hyperspherical space, with some applications in geometry and mathematical statisticsActa Mathematica, 1960
- ON THE MOMENTS OF ORDER STATISTICS IN SAMPLES FROM NORMAL POPULATIONSBiometrika, 1954