In this paper, we consider the stochastic ray production function that has been revived recently by Henningsen et al. (2017). We use a profit-maximizing framework to resolve endogeneity problems that are likely to arise, as in all distance functions, and we derive the system of equations after incorporating technical inefficiency. As technical inefficiency enters non-trivially into the system of equations and the Jacobian is highly complicated, we propose Monte Carlo methods of inference. We illustrate the new approach using US banking data and we also address the problems of missing prices and selection of ordering for outputs.