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Bivariate Normal Distribution Plots

4 messages · Jeff Reichman, S Ellison, Richard M. Heiberger +1 more

Original
Jeff 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
S Ellison
# 
Er, yes ... that is what you asked for.

Have you tried rho_xy=0.7 or similar in the code above?


*******************************************************************
This email and any attachments are confidential. Any use...{{dropped:8}}
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 at sbcglobal.net> wrote:
1 day later
Marc Girondot
# 
Try this code:

# 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))


Hope it helps,

Marc

Le 12/04/2018 ? 16:59, JEFFERY REICHMAN a ?crit?: