Given a ranking of size n , most of the existing ranking models have relatively small numbers of parameters (around n , or less). Having a small number of parameters do help facilitate the application of a ranking model. But on the other hand, it restricts the capacity for the model to describe the innate structure of a ranking population.  In this report, we suggest a random ranking generator with ( n - 1) 2 parameters. The increased number of parameters enables the generator to simulate ranking populations with greater flexibility. We also suggest the use of a n x n probability matrix (P-matrix) as a device for specifying the targeted ranking population. In the P-matrix, each cell is the probability of an item being assigned a certain rank. We provide an algorithm that estimates, from a given P-matrix, the parameters for the generator. Numerical examples show that using the P-matrix based parameter estimation algorithm, the proposed generator provides better simulation to the targeted rank data.