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
> -----Original Message----- > From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of JEFFERY REICHMAN> # 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) > ... > Problem is this results in sigma(x) = sigma(y), rho=0 ... > What I have created creates a circle.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}}
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:> 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
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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?:> 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
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>