Pure characteristics demand models is a utility-based choice model which is used to determine a consumer’s purchase decision among a list of available products and to provide an estimate of product demands. Under stochastic and distributionally robust environment, we consider the two challenge problems: the problem of estimating model parameters based on generalizd method of moments and the multiproduct pricing problem based on pure characteristics demand models. In stochastic case, the regularized sample average approximation method is used to handle the set-valued stochastic equilibrium constraints. In distributionally robust case, we use the regularization method and the data driven approach to handle the set-valued distributionally robust equilibrium constraints. The corresponding convergence analysis results are given and numerical results are reported to show that validate the effectiveness and scalability of our approach.