Invariance of the distribution of the maximum

Mogens Fosgerau, Per Olov Lindberg, Lars-Göran Mattsson and Jörgen Weibull

MPRA Paper from University Library of Munich, Germany

Abstract: Many models in economics involve probabilistic choices where each decision-maker selects the best alternative from a finite set. Viewing the value of each alternative as a random variable, the analyst is then interested in the choice probabilities, that is, the probability for an alternative to give the maximum value. Much analytical power can be gained, both for positive and normative analysis, if the maximum value is statistically independent of which alternative obtains the highest value. This note synthesizes and generalizes previous results on this invariance property. We provide characterizations of the property within a wide class of distributions that comprises the McFadden GEV class, show implications in several directions, and establish connections with copulas. We illustrate the usefulness of the invariance property by way of a few examples.

Keywords: Choice; random utility; extreme value; leader-maximum; invariance; independence (search for similar items in EconPapers)
JEL-codes: C1 C25 D01 (search for similar items in EconPapers)
Date: 2015
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https://mpra.ub.uni-muenchen.de/65206/1/MPRA_paper_65206.pdf revised version (application/pdf)

Related works:
Working Paper: Invariance of the distribution of the maximum (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:63529

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