The Quasi Monte Carlo (QMC) methods [1] are sequences that converge faster than Monte Carlo (MC) [2] because they use low discrepancy sequences with better uniformity properties. Refined Descriptive Sampling (RDS) [3] method was selected as one of the best sampling method used in a simulation study.
In this paper, we proceeded to the generation of QMC, MC and RDS samples from an exponential random variable then a comparison of the five sampling methods namely RDS, MC and QMC as Halton, Sobol and Faure was carried out. The methods of QMC, especially Sobol sequences, and the method of RDS have shown empirically the best results according to the both statistical criteria, the mean error and absolute error.
Keys words: Simulation, Monte Carlo, Quasi Monte Carlo, Sampling
References:
[1] Saliby, E. "An empirical evaluation of sampling methods in risk analysis simulation : Quasi-Monte Carlo, Descriptive sampling and Latin hypercube sampling", 2002.
[2] Owen, A. B. Monte Carlo, Quasi Monte Carlo, and Randomized Quasi Monte carlo. In H. Niederreiter and J. Spanier: Monte carlo and Quasi Monte Carlo methods, Springer,, 1998, pp. 86-97.
[3] Tari, M. Dahmani, A. Refined descriptive sampling: a better approach to Monte Carlo simulation. Simulation Modelling Practice and Theory. 2006; 14:143--160.