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ON THE PROBABILITY OF BEING MAXIMAL
Author(s) -
Li Deyuan
Publication year - 2008
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2008.00524.x
Subject(s) - gumbel distribution , mathematics , independent and identically distributed random variables , random variable , extreme value theory , cumulative distribution function , generalized extreme value distribution , combinatorics , probability distribution , domain (mathematical analysis) , discrete mathematics , probability density function , statistics , mathematical analysis
Summary Let X 1 , X 2 , … , 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.