Abstract
SummaryLet X1, X2, … , Xn be independent and identically distributed random variables with a continuous cumulative distribution function F, which belongs to the max‐domain of attraction of the Frechet or Gumbel extreme value distribution. We define the probability of being maximal, Dn, and approximate it. Several previous papers have considered this problem, but only for special cases. The approximations to Dn are very useful for obtaining demand functions from random utility models in the qualitative response models used in social sciences.
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