Bivariate plot of a bivariate normal distribution

An example:

# Standard deviations and correlation
sig_x <- 1
sig_y <- 2
rho_xy <- 0.7

# Covariance between X and Y
sig_xy <- rho_xy * sig_x *sig_y

# Covariance matrix
Sigma_xy <- matrix(c(sig_x ^ 2, sig_xy, sig_xy, sig_y ^ 2), nrow = 2, ncol = 2)

# Load the mvtnorm package
library("mvtnorm")

# Means
mu_x <- 0
mu_y <- 0

# Simulate 1000 observations
set.seed(12345)  # for reproducibility
xy_vals <- rmvnorm(1000, mean = c(mu_x, mu_y), sigma = Sigma_xy)

# Have a look at the first observations
head(xy_vals)

# Create scatterplot
# plot(xy_vals[, 1], xy_vals[, 2], pch = 16, cex = 2, col = "blue",
#      main = "Bivariate normal: rho = 0.0", xlab = "x", ylab = "y")

library(graphics)

x <- xy_vals[, 1]
y <- xy_vals[, 2]

par(mar=c(4, 4, 2, 6)+0.4)

smoothScatter(x, y, asp=1,
              main = paste("Bivariate normal: rho = ", rho_xy),
              xlab = "x", ylab = "y")


# Add lines
abline(h = mu_y, v = mu_x)

library(fields)

n <- matrix(0, ncol=128, nrow=128)

xrange <- range(x)
yrange <- range(y)

for (i in 1:length(x)) {
  posx <- 1+floor(127*(x[i]-xrange[1])/(xrange[2]-xrange[1]))
  posy <- 1+floor(127*(y[i]-yrange[1])/(yrange[2]-yrange[1]))
  n[posx, posy] <- n[posx, posy]+1
}

image.plot( legend.only=TRUE,
            zlim= c(0, max(n)), nlevel=128,
            col=colorRampPalette(c("white", blues9))(128))