[R] Bivariate Normal Distribution Plots

[Richard M. Heiberger]

Please look at my book
Statistical Analysis and Data Display
https://www.springer.com/us/book/9781493921218

Figures 3.8, 3.9, 3.10

The code for these figures is available in the HH package

install.packages("HH")
library(HH)
HHscriptnames(3) ## this gives the filename on your computer containing the code
## open the file in your preferred editor and run chunks 15 and 16


On Thu, Apr 12, 2018 at 10:59 AM, JEFFERY REICHMAN
<reichmanj using sbcglobal.net> wrote:
> 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
>
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