Practical Applications

hal 105

library(mvtnorm)
library(ggplot2)
library(matlib)

##Standard deviation
sigma <- matrix(c(4,2,2,3), ncol = 2, nrow = 2)
##Mean
mu <- c(1,2)

n <- 1000

set.seed(123)

x<- rmvnorm(n=n, mean=mu, sigma=sigma)

d <- data.frame(x)

p2 <- ggplot(d, aes(x = X1, y = X2)) +
  geom_point(alpha = .5) +
  geom_density_2d()

p2

y <- x- mu

E <- eigen(sigma)
E$vectors

##            [,1]       [,2]
## [1,] -0.7882054  0.6154122
## [2,] -0.6154122 -0.7882054

y <- y %*% t(inv(E$vectors))

dd <- data.frame(y)

p3 <- ggplot(dd, aes(x = X1, y = X2)) +
  geom_point(alpha = .5) +
  geom_density_2d()
p3