如何在R中创建具有特定相关性的正常随机变量？
要创建具有特定相关性的正常随机变量，我们可以使用MASS包的mvrnorm函数。例如，如果我们要创建两个大小为10的变量，其均值等于2和4，标准差为0.5，则可以使用以下命令来完成-
mvrnorm(10,mu=c(2,4),Sigma=matrix(c(1,0.5,0.5,1),ncol=2),empirical=TRUE)
例1
library(MASS) X<-mvrnorm(20,mu=c(5,6),Sigma=matrix(c(1,0.97,0.97,1),ncol=2),empirical=TRUE) X输出结果
[,1] [,2] [1,] 4.734045 5.860623 [2,] 3.844051 4.920516 [3,] 4.387584 5.769242 [4,] 5.720935 6.694407 [5,] 5.749076 6.905320 [6,] 4.814826 5.649758 [7,] 5.320584 6.716148 [8,] 5.791732 6.629848 [9,] 6.234083 7.088140 [10,] 4.209064 5.523264 [11,] 4.658825 5.334275 [12,] 6.499547 7.302753 [13,] 6.296104 6.828497 [14,] 4.203930 5.353094 [15,] 3.679087 4.464786 [16,] 3.547234 4.457977 [17,] 6.116487 7.273061 [18,] 4.872711 5.646771 [19,] 3.395766 4.340987 [20,] 5.924329 7.240531
cor(X)
[,1] [,2] [1,] 1.00 0.97 [2,] 0.97 1.00
例2
Y<-mvrnorm(20,mu=c(100,120),Sigma=matrix(c(1,-0.78,-0.78,1),ncol=2),empirical=TRUE) Y输出结果
[,1] [,2] [1,] 100.35035 119.5481 [2,] 98.80491 121.2622 [3,] 100.70750 118.3223 [4,] 100.87404 119.8765 [5,] 101.06911 119.1632 [6,] 99.80321 119.5711 [7,] 98.89158 120.5820 [8,] 98.63285 121.2333 [9,] 100.98014 120.7017 [10,] 98.20288 120.8348 [11,] 98.96695 121.0503 [12,] 99.97610 120.4775 [13,] 99.96563 119.2600 [14,] 100.59370 119.1507 [15,] 100.66358 119.3445 [16,] 101.25303 119.4787 [17,] 100.59732 119.3951 [18,] 99.67970 119.8449 [19,] 101.37637 118.6709 [20,] 98.61106 122.2320
cor(Y)
[,1] [,2] [1,] 1.00 -0.78 [2,] -0.78 1.00
范例3
Z<-mvrnorm(20,mu=c(1,1),Sigma=matrix(c(1,-0.40,-0.40,1),ncol=2),empirical=TRUE) Z输出结果
[,1] [,2] [1,] 0.344030694 1.10411548 [2,] 0.922039529 0.24012450 [3,] 0.631725557 2.00128990 [4,] 2.229289991 -0.50200549 [5,] 1.180211078 1.99181844 [6,] 1.012940481 1.49396082 [7,] 2.506394541 1.11997765 [8,] 1.019857403 -0.04125523 [9,] -0.004349292 -0.04837025 [10,] -0.770750258 2.35083803 [11,] -0.368335882 1.29590311 [12,] 1.338721298 2.92684775 [13,] 0.378076422 1.72233721 [14,] 2.650859368 -0.81180597 [15,] 1.355467066 0.37518755 [16,] 2.500790061 0.72880980 [17,] -0.619248618 1.58565187 [18,] 0.924785938 -0.10665410 [19,] 1.196351320 1.06036152 [20,] 1.571143303 1.51286741
cor(Z)
[,1] [,2] [1,] 1.0 -0.4 [2,] -0.4 1.0