More Efficient Approximation of Multiple Integrals using Steady State Ranked Simulated Sampling

This article extends the concept of using the steady state ranked simulated sampling approach (SRSIS) by Al-Saleh and Samawi (2000) for improving Monte Carlo methods for single integration problem to multiple integration problems. We demonstrate that this approach provides unbiased estimators and substantially improves the performance of some Monte Carlo methods for bivariate integral approximations, which can be extended to multiple integrals’ approximations. This results in a significant reduction in costs and time required to attain a certain level of accuracy. In order to compare the performance of our method with the Samawi and Al-Saleh (2007) method, we use the same two illustrations for the bivariate case.