Implementation of a Parallel Algorithm to Simulate the Type I Error Probability

Simulating the probability of type I error is a powerful statistical tool that allows confirming if the statistical test achieves the established nominal level. However, its computational implementation has the drawback of significantly long execution times. Therefore, this article analyzes the performance of two parallel implementations ( parRapply and boot ) which significantly reduce the execution time of simulations of type I error probability for a goodness-of-fit test for the bivariate Poisson distribution. The results obtained demonstrate how the parallelization strategies accelerate the simulations, reducing the time by 50% to 90% when using 2 to 12 processors running in parallel. This reduction is graphically evidenced as the execution time of the analyzed parallel versions fits almost perfectly ( R 2 ≈ 0.999 ) to the power model y = a p b , where p is the number of processors used, and a > 0 and b < 0 are the constants of the model. Furthermore, it is shown that the parallelization strategies used scale with an increasing number of processors. All algorithms were implemented in the R programming language, and their code is included at the end of this article.