Multinomial Logit model based on Gumbel Copula

For the IID (identically & independently distributed) condition of the multinomial Logit model, which requires all random terms existing in the utilities of alternatives to be independent each other, a discrete choice model was proposed, based on the Copula function which can be used to derive the joint probability distribution of multi-random variables. The IID condition is weakened and the distribution of the difference between every two random terms is obtained using the Gumbel Copula function's property. It is found that this distribution still follows the Logistic type but the difference must be multiplied by a parameter which can be estimated by the likelihood method from survey data. This result is then extended and employed in the discrete choice problem with more than two alternatives. The probability of choosing a specific alternative is rigorously formulated. The work surmounts the difficulty of applying the multinomial Logit model.