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I have a known multinomial distribution of a population due to a census. I want to compare a sample with this population. I want to know the probability that the same ranking of the classes of the multinomial is observed in the sample as in the population. Example: Assume there are 20 brands of wine. We know the market share of each brand. What is the probability of observing the most frequent brand as a the most frequent brand in a sample AND of the second most frequent brand as the second most frequent brand in the sample and so on up to the k-most frequent brand.

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  • $\begingroup$ What does "compating" in the title mean? Computing, competing, comparing, counting, ... ? $\endgroup$ – whuber Dec 28 '15 at 14:15
  • $\begingroup$ I meant "comparing ranks for a multinomial distribution". Sorry for the typo. The problem should be common in survey research, but I find no reference for it. The problem is part of an analysis of a frequency attack in a cryptographic setting. $\endgroup$ – user99590 Jan 3 '16 at 9:27

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