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. >