Abstract Minimization of relative entropy under fractile constraints is used to select a probability model for a random variable of unknown type, given only a random sample of independent observations of the variable. The fractile constraints replace the conventional moment constraints. They are based on the sample rule, an exact combinatorial relationship. The method selects one distribution in any candidate set that conveys the minimum amount of information about the variable, over and above the information contained in the sample. This model is best among the candidate distributions in an objective sense. The optimum reference distribution also minimizes the minimum relative entropy value relative to the sample; however, it does not in general satisfy the sample rule. But the method also yields a unique posterior distribution that does satisfy the sample rule. Together with the optimum reference distribution, this posterior minimizes the relative entropy, and in this sense it. too, can be considered as...