Enhancing the Performance of the Mont Carlo Simulation for Generating Correlated Data: An Application to Climate Change

The Mont Carlo simulation is widely used for data generation based on specified distribution. However, generation of correlated data is only possible for specific distributions (bivariate normal), while it is required to deal with non-normal distributions, e.g. in regional frequency analysis. To tackle the problem, an innovative approach was proposed by using the genetic algorithm. Since it is possible only to change the order of numbers in an array, our problem is not completely in agreement with the classic genetic algorithm. Therefore, we reordered the algorithm; the internal of each chromosome was changed instead of crossing two different ones. The proposed method was applied for one random variable, and it was shown that the genetic algorithm produces multi-solutions, while unique solution is obtained using the Mont Carlo simulation procedure. We presented an appropriate objective function to include any bivariate distribution and showed its hither versatility as compared with the Mont Carlo simulation (only for the bivariate normal distribution). The multi-solutions in our proposed methodology is due to the fact that any array can be reordered in different possible combinations, each of which having a unique correlation coefficient with another fixed array. It was shown that these different combinations increase as the correlation coefficient decreases.