A note on the invariance of the distribution of the maximum
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A note on the invariance of the distribution of the maximum. / Fosgerau, Mogens; Lindberg, Per Olov; Mattsson, Lars Göran; Weibull, Jörgen.
I: Journal of Mathematical Economics, Bind 74, 01.2018, s. 56-61.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - A note on the invariance of the distribution of the maximum
AU - Fosgerau, Mogens
AU - Lindberg, Per Olov
AU - Mattsson, Lars Göran
AU - Weibull, Jörgen
PY - 2018/1
Y1 - 2018/1
N2 - 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.
AB - 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.
KW - Discrete choice
KW - Extreme value
KW - Invariance
KW - Leader-maximum
KW - Random utility
U2 - 10.1016/j.jmateco.2017.10.005
DO - 10.1016/j.jmateco.2017.10.005
M3 - Journal article
VL - 74
SP - 56
EP - 61
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
SN - 0304-4068
ER -
ID: 199173597