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Invariance of the distribution of the maximum
KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport Planning, Economics and Engineering. KTH, School of Architecture and the Built Environment (ABE), Centres, Centre for Transport Studies, CTS.
KTH, School of Architecture and the Built Environment (ABE), Transport Science. KTH, School of Architecture and the Built Environment (ABE), Centres, Centre for Transport Studies, CTS.
KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport Planning, Economics and Engineering. KTH, School of Architecture and the Built Environment (ABE), Centres, Centre for Transport Studies, CTS.ORCID iD: 0000-0001-9507-9185
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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 this 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.

Keyword [en]
choice, random utility, extreme value, leader-maximum, invariance, independence
National Category
Economics
Identifiers
URN: urn:nbn:se:kth:diva-164895OAI: oai:DiVA.org:kth-164895DiVA: diva2:806435
Funder
Knut and Alice Wallenberg Foundation
Note

QS 2015

Available from: 2015-04-20 Created: 2015-04-20 Last updated: 2015-11-17Bibliographically approved

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Mattsson, Lars-Göran

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Fosgerau, MogensLindberg, Per OlovMattsson, Lars-GöranWeibull, Jörgen
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Transport Planning, Economics and EngineeringCentre for Transport Studies, CTSTransport ScienceMathematics (Dept.)
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  • fi-FI
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Output format
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