Perhaps the most obvious assump tion to make is that the e's are distributed multinomially assumption generates what is known as a probit model. Unfortunately,
multinomial probit mod els cannot be expressed easily in an analytically closed form [Daganzo. 1979] and hence are computationally cumbersome and expensive to use.
the e's is that they are
An alternative assumption concerning the distribution o each independently and identically distributed (iid) with a Gumbel Type I distribu- tion whose cumulative distribution function is given by
Choosing this particular distribution is motivated entirely by considerations of analytical convenience, since when Eq. [5.22] is integrated in order to evaluate