On the efficiency of partition pseudo random number generated in integral estimation

Abstract

We know the Monte Carlo method for high number of samples is an unbiased estimator, as well as converges with slowly speed. To address this problem,  quasi- Monte Carlo methods were introduced. Quasi-Monte Carlo method has good efficiency and strong convergence, but as the dimension of the problem increases, the advantage of quasi-Monte Carlo method quickly decreases, and the error of quasi-Monte Carlo increases, so. To solve this problem, we use the hybrid Monte Carlo method. Hybrid Monte Carlo is composed of hybrid sequence. Hybrid sequence is a combination of Monte Carlo, quasi-Monte Carlo and randomize quasi-Monte Carlo. In this we use hybrid Monte Carlo method using Halton sequence based on partitioning the interval Monte Carlo method using Halton sequence based on partitioning the interval  to k subintervals and control the number to follow must possible informity on . Also, as an alternative, we use scramble on Halton sequence to increase the unifotmity on the all areas of desired sections whole parts.