An ordering of dependence for distribution of k-tuples, with applications to lotto games. (English) Zbl 0632.62048
A majorization ordering is defined over the class of distributions of k- tuples from \(\{\) 1,...,N\(\}\) with the same vector of marginal frequencies of occurrences for the integers from 1 to N. Results are obtained for the maximal and minimal distributions with respect to this ordering. Applications to lotto games and election results are presented; for Lotto 6/49, an estimate of the distribution of 6-tuples is given, based on data on the marginal frequencies of the numbers 1 to 49.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62H99 | Multivariate analysis |
| 06A06 | Partial orders, general |
| 62P99 | Applications of statistics |
Keywords:
convexity; extreme points; majorization ordering; distributions of k- tuples; marginal frequencies; maximal and minimal distributions; lotto games; election resultsReferences:
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