On the effect of inducted negative correlation rate for beta acceptance–rejection algorithms

ABSTRACT

One of the variance reduction methods in simulation experiments is negative correlation induction, and in particular the use of the antithetic variates. The simultaneous use of antithetic variates and an acceptance–rejection method has been studied in some papers, where the inducted negative correlation has been calculated. In this study, the factors affecting the inducted negative correlation rate are addressed. To do this, the beta distribution is first selected to generate negatively correlated random variates using the acceptance–rejection method. The effects of both the efficiency of the acceptance–rejection method and the initial negative correlation rate on the inducted negative correlation are explored. Results show that both factors have significant effects; therefore, a combination of both can lead to algorithms better able to generate negative correlations.

KEYWORDS:

• Acceptance–rejection method
• Antithetic Variates
• Beta distribution
• Negative correlation induction

MATHEMATICAL SUBJECT CLASSIFICATION:

• Primary 68U20
• Secondary 65C10

Acknowledgments

The authors are thankful for the constructive comments of anonymous reviewer.

Notes

1 r₁ is the Pearson product moment correlation coefficient; a dimensionless index that ranges from −1.0 to 1.0 inclusive and reflects the extent of a linear relationship between two data sets.