Clark D E, el-Taha M
Department of Surgery, Maine Medical Center, Portland, USA.
Methods Inf Med. 1998 Sep;37(3):235-8.
A Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.
逻辑正态随机变量（Y）由正态随机变量（X）通过关系Y = (e^X)/(1 + e^X)得到。在决策树的蒙特卡罗分析中，逻辑正态随机变量可用于对分支概率进行建模。在某些情况下，要建模的概率可能不是独立的，因此生成相关逻辑正态随机变量的方法会很有用。之前已经描述了一种生成相关正态随机变量的技术。利用泰勒级数近似以及方差和协方差的代数定义，我们描述了估计正态随机变量的均值、方差和协方差的方法，这些正态随机变量在使用上述公式进行变换后，将得到具有近似所需均值、方差和协方差的逻辑正态随机变量。使用Mathematica计算机代数系统对该方法进行的多次模拟显示，其与理论结果吻合良好。
