An Empirical Comparison of Monte Carlo Methods for Simulating Random Variants that follow Cubic Polynomial Based Mathematical Models

摘要

This paper comnpares the run times of several algorithms for simulating random variants of cubic polynomials using several common Monte Carlo methods. Five methods for simulating diverse experimental data sets using cubic polynomial based models were explored. It was found that the choice of which algorithm to implement depends on the shape and type of underlying mathematical model. Several benchmarks indicated that the rejection Monte Carlo method out performs the other algorithms in most cases, and the inversion Monte Carlo method, using the quartic formula as the inversion algorithm, offers the most consistent performance, and even outperforms the rejection Monte Carlo algorithm in some cases.