Note—A Note on “Efficiency of the Antithetic Variate Method for Simulating Stochastic Networks”
针对Sullivan等人关于PERT网络对偶抽样方差缩减的定理，将其适用范围从对称分布扩展到任意弧时间分布，证明了方差缩减的普遍性。
In a recent paper by Sullivan, Hayya, and Schaul (Sullivan, R. S., J. C. Hayya, R. Schaul. 1982. Efficiency of the antithetic variate method for simulating stochastic networks. Management Sci. 28 (5, May) 563–572.), they present a theorem which proves that negative covariance will be guaranteed, and thus a variance reduction achieved, when estimating the project completion time in PERT networks using antithetic sampling procedures. Their proof is restricted to stochastic networks in which the arc time distributions are symmetric about their means. In this note we present a proof which guarantees a variance reduction for arbitrary arc time distributions.