请问如何生成三组correlation不等於零的uniform random variable

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请问如何生成三组uniform random variable (x, Y, Z)且Corr(X,Y)不等於零，Corr(X,Z)不等於零，Corr(Y,Z)不等於零？谢谢

下面为生成两组correlation不等於零的uniform random variable。
This can be implemented by the following code:  n  <- 100  p  <- 0.6            # (say)  X  <- runif(n)-1/2  Z  <- runif(n)-1/2  U  <- rbinom(n,1,p)  # =1 where Y=X, = 0 when Y independent of X  Y  <- X*U + Z*(1-U)  XY <- cbind(X,Y)     # your n by 2 matrix of bivariate (X,Y)Now the marginal distributions of X and Y are both uniform.var(X) = 1/12 and var(Y) = 1/12. Since the means are 0,cov(X,Y) = Exp(X*Y) = p*Exp(X^2) = p/12cor(X,Y) = cov(X,Y)/sqrt(var(X)*var(Y)) = (p/12)/(1/12) = p.So all you need to do to get a desired correlation rho betweenX and Y is to set p = rho.

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关键词：correlation Variable relation Uniform random following 如何

# generate normals, check correlations
X <- array(rnorm(9000), dim = c(3000, 3))
cor(X)
# desired correlation
M <- c(1.0, 0.9, 0.6, 0.9, 1.0, 0.3, 0.6, 0.3, 1.0)
dim(M) <- c(3,3)
M
#     [,1] [,2] [,3]
#[1,]  1.0  0.9  0.6
#[2,]  0.9  1.0  0.3
#[3,]  0.6  0.3  1.0
# adjust correlations for uniforms
for (i in 1:3){
    for (j in 1:3){
        if (i != j){
            M[i, j] <- 2 * sin(pi * M[i, j] / 6)
            M[j, i] <- 2 * sin(pi * M[j, i] / 6)
        }
    }
}
# induce correlation, check correlations
C <- chol(M)
Y <- X %*% C
cor(Y)
# create uniforms, check correlations
Y <- pnorm(Y)
cor(Y)
x=Y[,1]
y=Y[,2]
z=Y[,3]
cor(x,y)    #0.9102382
cor(y,z)    #0.3213543
cor(x,z)    #0.6197905
# plot results (marginals)
par(mfrow = c(1,3))
hist(x, main = paste("x"), xlab = "")
hist(y, main = paste("y"), xlab = "")
hist(z, main = paste("z"), xlab = "")
  

epoh 发表于 2011-11-2 19:13
# generate normals, check correlations
X

很详细，谢谢。