More Efficient Monte Carlo Methods Obtained by Using Ranked Set Stimulated Sample

Estimation of integrals by crude Monte Carlo methods, using uniform simulated sample (USS) required a large sample size to achieve high accuracy. Reduction in sample size is achieved using USS with the sophisticated Monte Carlo methods such as antithetic, importance or control variate sampling. In this paper, we show that the performance of these methods is substantially improved by using ranked simulated samples (RSIS) in place of USS. This results in a very large saving in of simulated sample size and hence in cost and time. We show that the modified methods using RSIS provide unbiased estimators for the integrals. Some characteristics and theoretical concepts of RSIS are given. A simulation study is conducted to compare the performance of the methods using RSIS to USS.