[R] Bivariate Normal Distribution Plots

[JEFFERY REICHMAN]

R-Help

I am attempting to create a series of bivariate normal distributions.  So using the mvtnorm library I have created the following code ...

# Standard deviations and correlation
sig_x <- 1
sig_y <- 1
rho_xy <- 0.0

# 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")

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

Problem is this results in sigma(x) = sigma(y), rho=0 and I need or what 2sigma(x)=sigma(y), rho=0 or 2sigma(y)=sigma(x), rho=0 to elongate the distribution.  What I have created creates a circle.  Can I do that within the mvtnorm package?

Jeff Reichman