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Choice Probabilities in Random Utility Models: Necessary and Sufficient Conditions for a Much Used Formula, andImplications for the Conditional Distributions of Achieved Utility
KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
2012 (English)Report (Other academic)
Abstract [en]

Random Utility (RU) Models have reached a wide applicability in many areas of applied Economics. In all application areas, the formulas for the choice probabilities play a central role. For the formulas to be useful, the probabilities further need to sum up to 1. In this note, we give necessary and sufficient conditions for the validity of the classical choice probability formula (i.e. that the choice probabilities are the integrals of the partial derivatives of the cdf of the random term along the diagonal), and that the probabilities sum up to 1. Further, it is proved sufficient that the gradient of said cdf is continuous and piecewise differentiable with locally bounded gradient, along the diagonal. Along the way we prove many intermediate results relating different derivatives of the cdf. Finally the results are applied to derive formulas for the distribution of achieved utility conditioned on a given alternative being chosen.

Place, publisher, year, edition, pages
2012.
National Category
Transport Systems and Logistics
Identifiers
URN: urn:nbn:se:kth:diva-95397OAI: oai:DiVA.org:kth-95397DiVA: diva2:528086
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
In thesis
1. Contributions to Probabilistic Discrete Choice
Open this publication in new window or tab >>Contributions to Probabilistic Discrete Choice
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. x, 20 p.
Series
TRITA-TSC-PHD, 12:001
National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95402 (URN)978-91-85539-86-4 (ISBN)
Public defence
2012-06-01, D2, Lindstedtsvägen 5, KTH, Stockholm, 09:15 (English)
Opponent
Supervisors
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note

QC 20120524

Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2016-01-20Bibliographically approved

Open Access in DiVA

fulltext(984 kB)130 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf