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A note on the invariance of the distribution of the maximum
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.ORCID iD: 0000-0001-9507-9185
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Stockholm School of Economics, Sweden.
2018 (English)In: Journal of Mathematical Economics, ISSN 0304-4068, E-ISSN 1873-1538, Vol. 74, p. 56-61Article in journal (Refereed) Published
Abstract [en]

Many models in economics involve discrete choices where a decision-maker selects the best alternative from a finite set. Viewing the array of values of the alternatives as a random vector, the decision-maker draws a realization and chooses the alternative with the highest value. The analyst is then interested in the choice probabilities and in the value of the best alternative. The random vector has the invariance property if the distribution of the value of a specific alternative, conditional on that alternative being chosen, is the same, regardless of which alternative is considered. This note shows that the invariance property holds if and only if the marginal distributions of the random components are positive powers of each other, even when allowing for quite general statistical dependence among the random components. We illustrate the analytical power of the invariance property by way of examples.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 74, p. 56-61
Keywords [en]
Discrete choice, Extreme value, Invariance, Leader-maximum, Random utility
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-219633DOI: 10.1016/j.jmateco.2017.10.005ISI: 000424736800005Scopus ID: 2-s2.0-85035079879OAI: oai:DiVA.org:kth-219633DiVA, id: diva2:1164399
Funder
Knut and Alice Wallenberg Foundation, KAW 2002.0199EU, European Research Council, 740369
Note

QC 20171211

Available from: 2017-12-11 Created: 2017-12-11 Last updated: 2018-03-05Bibliographically approved

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Mattsson, Lars-Göran

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