Author(s)

Dennis Ridley^1,2, Pierre Ngnepieba³

¹School of Business & Industry, Florida A&M University, Tallahassee, FL, USA.
²Department of Scientific Computing, Florida State University, Tallahassee, FL, USA.
³Department of Mathematics, Florida A&M University, Tallahassee, FL, USA.

A traditional method of Monte Carlo computer simulation is to obtain uniformly distributed random numbers on the interval from zero to one from a linear congruential generator (LCG) or other methods. Random variates can then be obtained by the inverse transformation technique applied to random numbers. The random variates can then be used as input to a computer simulation. A response variable is obtained from the simulation results. The response variable may be biased for various reasons. One reason may be the presence of small traces of serial correlation in the random numbers. The purpose of this paper is to introduce an alternative method of response variable acquisition by a power transformation applied to the response variable. The power transformation produces a new variable that is negatively correlated with the response variable. The response variable is then regressed on its power transformation to convert the units of the power transformed variable back to those of the original response variable. A weighted combination of these two variables gives the final estimate. The combined estimate is shown to have negligible bias. The correlations of various antithetic variates obtained from the power transformation are derived and illustrated to provide insights for this research and for future research into this method.

Inverse Correlation, Variance Reduction, Antithetic Random Variates, Simulation Model Bias, Bias Reduction

Ridley, D. and Ngnepieba, P. (2023) Antithetic Power Transformed Random Variables in Computer Simulations: An Error Correction Mechanism. Journal of Applied Mathematics and Physics, 11, 1707-1727. doi: 10.4236/jamp.2023.116111.