Developing Multidimensional Pseudo-Random Number Generation Methods to Reproduce Correlations including Nonlinear Correlations

M. Hosoi and Y. Uchida (Japan)


Random Number Generation, Statistical and ProbabilisticModeling, Simulation Uncertainty, Numerical ProbabilityDistribution Method, Computational Statistics


To obtain appropriate and valid results of simulations, initial and parameter values in simulations need to be set based on observed samples. However, observed sample data has the following characteristics frequently: (1) the number of samples being observed is small; (2) the population distribution of the data is unknown; and (3) in many cases, the variables are not independent, and there are linear or nonlinear relationships among observed samples. In these cases, it is difficult to generate pseudo random numbers based on observed samples by existing methods. We developed new multidimensional pseudo random number generation methods employing continuous bootstrap methods that make use of a numerical probability distribution table. By use of this method, it becomes possible to generate multidimensional pseudo-random numbers that reproduce any correlation including nonlinear correlations using any sample size, while preserving the complex relationship among variables of the samples. In this paper, we presented the algorithm of our new pseudo-random number generation method and numerical calculation examples, and then indicated that this pseudo-random number generation method is practical.

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