Abstract
The construction of J-variate distribution functions, introducing dependences among J random variables and keeping fixed the J marginal distribution functions, is important in the development of theoretical and empirical statistical analysis. Here, a method for generating such distribution functions is developed. Characteristics of the resulting distribution functions are discussed. An application to discrete regression models is presented. The latter is specialized to model choice of mode od transportation by travelers.
Highlights
In the development of probabilistic model and statistical analysis, the postulation of a joint cumulative distribution function (JCDF), keeping fixed some marginal cumulative distributions (MCDF), is often required (Yadlin, 1991; Long and Krysztofowicz, 1995)
If there are J components functioning in parallel, the formulation of a JCDF for the Dj, J = 1, . . . , J, with exponential MCDF, that becomes the product of these MCDF under restrictions, may be convenient (Sarkar, 1987)
If there are J ≥ 2 stimuli, J tolerance functions, Tr(1), Tr(2), . . . , Tr(J) associated to the rth response, a JCDF, with Logistic MCDF for the Tr(j), which becomes the product of these marginal Logistics under restrictions may be established
Summary
In the development of probabilistic model and statistical analysis, the postulation of a joint cumulative distribution function (JCDF), keeping fixed some marginal cumulative distributions (MCDF), is often required (Yadlin, 1991; Long and Krysztofowicz, 1995). In dosage-response models, it is assumed that there exists a random tolerance function Tr, r = 1, . Tr(J) associated to the rth response, a JCDF, with Logistic MCDF for the Tr(j), which becomes the product of these marginal Logistics under restrictions may be established. In discrete decision models (DDM), it is assumed that there exists a radom utility functions Um = i = 1, . A Nesting MLM, that overcomes the latter drawback, can be obtained by constructing a Nesting EV JCDF that keeps the J MCDF as EV This Nesting MLM is consistent with the principle of utility maximization, exhibits a closed functional form manageable for theoretical and empirical investigations, and allows for the introduction of relations among alternatives through the inclusion of a dependence parameter. Since MI ⊂ M ; likelihood methods can be applied to test MI versus M
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