Abstract
Randomness for a statistician must have some structure. In traditional combinatorics the word random means uniform distribution on a set which may be the set of all graphs with n vertices, the set of all permutations of the numbers N = (1,2,..., n), the set of all partitions of N, or any other set of simple structure. In practice the statistician meets a subset of the structures and she or he is interested in the question, what was the mechanism which generated the sample. Uniform distribution and independence are shapeless and they have low complexity for catching the character of samples produced by real life situations. In [12] Persi Diaconis investigated a sample consisting of the votes in an election of the American Psychological Association. The sample was investigated by others but without achieving a reasonable goodness of fit, because the present collection of distribution of permutations is not large enough. Investigating the sample we found a hidden property leading to a new class of distributions of permutations.
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© 2008 János Bolyai Mathematical Society and Springer-Verlag
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Csiszár, V., Rejtő, L., Tusnády, G. (2008). Statistical Inference on Random Structures. In: Győri, E., Katona, G.O.H., Lovász, L., Sági, G. (eds) Horizons of Combinatorics. Bolyai Society Mathematical Studies, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77200-2_2
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