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Bivariate Normal Distribution Plots

 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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Re: Bivariate Normal Distribution Plots

 > -----Original Message----- > From: R-help [mailto:[hidden email]] 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}} ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.