Abstract: The probability density evolution method (PDEM) provides a feasible approach for nonlinear stochastic response analysis of multi-degree-of-freedom systems. In the present paper, the point evolution, ensemble evolution and the partition of probability-assigned space are firstly revisited. The criterion for point selection is then explored. The concept of generalized F-discrepancy (GF-discrepancy), which avoids the NP-hard problem of computation, is introduced for random variables of general non-uniform, non-Gaussian distribution as an index to measure the quality of a point set. The relationship between GF-discrepancy and EF-discrepancy is explored and the error bound is studied by the extended Koksma-Hlawka inequality. Based on the GF-discrepancy, a new strategy for point-selecting and space-partitioning is proposed. The numerical example shows that the proposed method enables highly accurate probability density evolution analysis of nonlinear structures involving dozens of non-uniform random variables. Problems to be further studied are discussed.