ON THE PROBABILITY OF BEING MAXIMAL

Let X₁, X₂, … , X_n 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, D_n , and approximate it. Several previous papers have considered this problem, but only for special cases. The approximations to D_n are very useful for obtaining demand functions from random utility models in the qualitative response models used in social sciences.