Random Number Generation Using Low Discrepancy Points

Random uniform numbers in the range [0, 1) are used to invert the distributions of DFA variables and generate realized values. They are also perhaps the most often overlooked “parameters” of a DFA model. As the number of variables to simulate goes up, the number of iterations needed to reach satisfactory convergence increases as well. With a spreadsheet-based model the run times can become prohibitive, forcing a tradeoff between run time and accuracy of the answers. Low discrepancy points (LDPs) (also known as “quasi-random” sequences or Latin Hypercube) attempt to generate the random numbers in a systematic fashion such that the multi-dimensional space (hypercube) of uniform numbers is filled out with as little discrepancy as possible given the number of iterations. This paper will discuss several well-known methods for generating LDPs, and give a complete working example to generate Faure points, one variation of LDPs, including an Excel 97 spreadsheet with the complete Faure point generation algorithm in Visual Basic for Applications (VBA). This spreadsheet will be offered to the CAS website download library. It will also present results of performance tests of LDP’s against Excel-generated random numbers using theoretical distributions (Pareto, Poisson, lognormal, uniform and normal variables).