Multivariate Extreme Value Distributions and Coverage of Ranking Probabilities

Area of Science:

• Econometrics
• Probability Theory
• Decision Theory

Background:

• Random utility models are foundational in discrete choice analysis.
• Approximating ranking probabilities is crucial for understanding complex decision-making.
• Previous work established limitations on the types of distributions that could be approximated.

Purpose of the Study:

• To demonstrate the universal approximation capability of multivariate extreme value distributions within random utility models.
• To extend existing theoretical results concerning the scope of random utility models.

Main Methods:

• Utilizing the framework of multivariate extreme value distributions.
• Applying these distributions as random utility models.
• Analyzing their capacity to represent diverse ranking probability distributions.

Main Results:

• The class of multivariate extreme value distributions can approximate any ranking probability distribution.
• This result generalizes Theorem 1 from Dagsvik (1995).

Conclusions:

• Multivariate extreme value distributions offer a comprehensive tool for modeling choice behavior.
• The findings broaden the applicability of random utility models in econometrics and related fields.