Publication

Normalization of network generalized extreme value models

Jeffrey Newman
2008
Journal Articles

Abstract

Generalized extreme value (GEV) models provide a convenient way to model choice behavior that is consistent with utility maximization theory, but the development of specific new models within the GEV family has been slow, due to the difficulty of ensuring new formulations comply with all the GEV rules. The network GEV structure introduced by Daly and Bierlaire [Daly, A. and M. Bierlaire, 2006. A general and operational representation of Generalised Extreme Value models. Transportation Research Part B, v. 40, pp. 285-305.] provides a tool to quickly generate new models in the GEV family, without the burden of complex analysis of the new model to ensure its properties. This paper further develops the network GEV tool, describing several methodologies for correctly normalizing the allocation parameters in such models, to ensure unbiasedness. These methods vary depending on the structure of the underlying network.

Official source

https://infoscience.epfl.ch/entities/publication/0a71ca3b-7f1c-4cd0-a59d-af1edd142811

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Jeffrey Newman
2008
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0a71ca3b-7f1c-4cd0-a59d-af1edd142811

About this result

Related concepts (30)

Generalized extreme value distribution

In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables.

Tool

A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.

Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.

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