A note on the invariance of the distribution of the maximum

Mogens Fosgerau; Per Olov Lindberg; Lars Göran Mattsson; Jörgen Weibull

doi:10.1016/j.jmateco.2017.10.005

A note on the invariance of the distribution of the maximum

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

2 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Mathematical Economics
Vol/bind	74
Sider (fra-til)	56-61
ISSN	0304-4068
DOI	https://doi.org/10.1016/j.jmateco.2017.10.005
Status	Udgivet - jan. 2018

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10.1016/j.jmateco.2017.10.005

http://www.mendeley.com/research/note-invariance-distribution-maximum

Citationsformater

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title = "A note on the invariance of the distribution of the maximum",

abstract = "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.",

keywords = "Discrete choice, Extreme value, Invariance, Leader-maximum, Random utility",

author = "Mogens Fosgerau and Lindberg, {Per Olov} and Mattsson, {Lars G{\"o}ran} and J{\"o}rgen Weibull",

year = "2018",

month = jan,

doi = "10.1016/j.jmateco.2017.10.005",

language = "English",

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pages = "56--61",

journal = "Journal of Mathematical Economics",

issn = "0304-4068",

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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

SN - 0304-4068

VL - 74

SP - 56

EP - 61

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

ER -

A note on the invariance of the distribution of the maximum

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