Abstract: The principle of maximum entropy (POME), a non-parametric inference technique with complete mathematical framework, has been increasingly applied in water resources. POME is substantially an optimization problem and the probability density function (PDF) is derived with forms of constraints. However, previous studies have focused little attention on constraints that are in form of moments, subjectively specifying the order of moments, which may have limitations in determining optimal POME distributions. The main contribution of this study is to present a POME framework considering the optimal order of moments, with analyses of the convergence of different moments with common distributions and a theoretical-empirical approach determining the optimal order of moments. This technique has been applied with hydrological data collected from the Yangtze River and the Yellow River. The series simulated with the technique is analyzed by comparison with measured series. Results indicate a good performance with all the measured statistics falling within the boxplot.