On a conjecture by Ben-Akiva and Lerman about the nested logit model

07/20/2019
by   Alfred Galichon, et al.
NYU college
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We prove a conjecture of Ben-Akiva and Lerman (1985) regarding the random utility representation of the nested logit model, using a result of Pollard (1948).

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References

  • [1] Ben-Akiva, M. (1973). The structure of travel demand models. PhD thesis, MIT.
  • [2] Ben-Akiva, M., and Lerman, S. (1985). Discrete Choice Analysis: Theory and Application to Travel Demand. MIT Press.
  • [3] Bochner, S. (1937). “Completely monotone functions of the Laplace operator for torus and sphere.” Duke Math. J. vol. 3, pp. 488-502.
  • [4] Dishon, M. and Bendler, J. (1990). “Tables of the inverse Laplace transform of the function $ e^{-s^beta} $.” Journal of Research of the National Institute of Standards and Technology 95, pp. 433–467.
  • [5] Feller, W. (1971).

    An Introduction to Probability Theory and its Applications

    vol. 2, 2nd edition. Wiley.
  • [6] Humbert, P. (1945). “Nouvelles correspondances symboliques”. Bulletin de la Société Mathématique de France 69, pp. 121–129.
  • [7]  McFadden, D. (1978). “Modeling the choice of residential location”. In A. Karlquist et. al., editor, Spatial Interaction Theory and Residential Location. North Holland.
  • [8] Pollard, H. (1946). “The representation of $ e^{-x^lambda} $ as a Laplace integral”. Bulletin of the American Mathematical Society 52(10), pp. 908–910.
  • [9] Ridout, M. S. (2009). “Generating random numbers from a distribution specified by its Laplace transform”. Statistics and Computing 19, pp 439–450.
  • [10] Tiago de Oliveira, J. (1958). “Extremal Distributions”. Revista de Faculdada du Ciencia, Lisboa, Serie A, Vol. 7, pp. 215–227.
  • [11] Tiago de Oliveira, J. (1997). Statistical analysis of the extreme. Pendor.