Three-Point Approximations for Continuous Random Variables
比较了多种用于估计连续随机变量均值和方差的近似方法，重点研究三点近似。数值测试表明，PERT和三角密度函数等流行方法精度较差，而一种基于Pearson和Tukey工作的新三点近似在贝塔分布和狄利克雷分布测试中表现显著更优，可作为现有方法的替代方案。
This paper compares a number of approximations used to estimate means and variances of continuous random variables and/or to serve as substitutes for the probability distributions of such variables, with particular emphasis on three-point approximations. Numerical results from estimating means and variances of a set of beta distributions indicate surprisingly large differences in accuracy among approximations in current use, with some of the most popular ones such as the PERT and triangular-density-function approximations faring poorly. A simple new three-point approximation, which is a straightforward extension of earlier work by Pearson and Tukey, outperforms the others significantly in these tests, and also performs well in related multivariate tests involving the Dirichlet family of distributions. It offers an attractive alternative to currently used approximations in a variety of applications.