Fosgerau, Mogens and Lindberg, Per Olov and Mattsson, LarsGöran and Weibull, Jörgen (2015): Invariance of the distribution of the maximum.

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Abstract
Many models in economics involve probabilistic choices where each decisionmaker 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.
Item Type:  MPRA Paper 

Original Title:  Invariance of the distribution of the maximum 
Language:  English 
Keywords:  Choice; random utility; extreme value; leadermaximum; invariance; independence 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C25  Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles 
Item ID:  63538 
Depositing User:  Prof. Mogens Fosgerau 
Date Deposited:  10 Apr 2015 20:36 
Last Modified:  07 Oct 2019 17:22 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/63538 