1.2.1 The Inverse Transform Method 口连续型场合 生成随机数的逆变换方法是基于以下熟知的定理 Theorem1(Probability Integral Transformation).若X为连续型随机变 量，其cd为Fx,则U=Fx'(X)~U(0,1). Proof.定义 Fx(u)=inf{z:Fx(x)=u},0<u<1. 若随机变量U~U(0,1),则对所有x∈R,有 P(Fx'(U)≤x)=P(inf{t:Fx(t)=U}≤x) P(U<Fx(x))=FU(Fx(x))=Fx(x). 因此F(U)和随机变量X同分布. ▣ Previous Next First Last Back Forward 61.2.1 The Inverse Transform Method ❏ ÎY.|‹ )§ëÅÍ_CÜê{¥ƒu±eŸ½n Theorem 1 (Probability Integral Transformation). eXèÎY.ëÅC ˛, Ÿcdf èFX, K U = F −1 X (X) ∼ U(0, 1). Proof. ½¬ F −1 X (u) = inf{x : FX(x) = u}, 0 < u < 1. eëÅC˛U ∼ U(0, 1), Kȧkx ∈ R, k P(F −1 X (U) ≤ x) = P(inf{t : FX(t) = U} ≤ x) = P(U ≤ FX(x)) = FU (FX(x)) = FX(x). œdF −1 X (U)⁄ëÅC˛X”©Ÿ. Previous Next First Last Back Forward 6