An algorithm for improving the behavior of strings of pseudo-random numbers for variance reduction in sampling from Gamma distribution

This research effort attempts to investigate the conditions under which better variance reduction can be achieved in simulation of a system where random deviates are generated by the acceptance-rejection technique. To induce correlation among the generated deviates, both antithetic and stratified sampling will be considered to study the magnitude of variance reduction in estimating the renewal function for a single component replacement process with Gamma distributed life. The negative exponential and the Cheng enveloping functions will be considered and all four combinations of correlation induction-enveloping function will be tested. We will propose the correct approach in incorporating streams of pseudorandom numbers in the variance reduction algorithms which use a single random number stream to guarantee their uniform distribution as well as the correct correlation for various values of Gamma shape parameters. We consider a much wider spectrum of values for the Gamma shape parameter and propose an algorithm on whose basis a higher degree of variance reduction can be attained.