# Not Just Normal... Gaussian

[caption id=“” align=“alignleft” width=“188” caption=“Pretty Normal”] [/caption]

Dave, over at The Revolutions Blog, posted about the big ‘ol list of graphs created with R that are over at Wikimedia Commons. As I was scrolling through the list I recognized the standard normal distribution from the Wikipedia article on the same topic.

Below is the fairly simple source code with lots of comments. Here’s the source. Run it at home… for fun and profit.

> > # # External package to generate four shades of blue > # library(RColorBrewer) > # cols <- rev(brewer.pal(4, "Blues")) > cols <- c("#2171B5", "#6BAED6", "#BDD7E7", "#EFF3FF") > > # Sequence between -4 and 4 with 0.1 steps > x <- seq(-4, 4, 0.1) > > # Plot an empty chart with tight axis boundaries, and axis lines on bottom and left > plot(x, type="n", xaxs="i", yaxs="i", xlim=c(-4, 4), ylim=c(0, 0.4), > bty="l", xaxt="n", xlab="x-value", ylab="probability density") > > # Function to plot each coloured portion of the curve, between "a" and "b" as a > # polygon; the function "dnorm" is the normal probability density function > polysection <- function(a, b, col, n=11){ > dx <- seq(a, b, length.out=n) > polygon(c(a, dx, b), c(0, dnorm(dx), 0), col=col, border=NA) > # draw a white vertical line on "inside" side to separate each section > segments(a, 0, a, dnorm(a), col="white") > } > > # Build the four left and right portions of this bell curve > for(i in 0:3){ > polysection( i, i+1, col=cols[i+1]) # Right side of 0 > polysection(-i-1, -i, col=cols[i+1]) # Left right of 0 > } > > # Black outline of bell curve > lines(x, dnorm(x)) > > # Bottom axis values, where sigma represents standard deviation and mu is the mean > axis(1, at=-3:3, labels=expression(-3*sigma, -2*sigma, -1*sigma, mu, > 1*sigma, 2*sigma, 3*sigma)) > > # Add percent densities to each division, between x and x+1 > pd <- sprintf("%.1f%%", 100*(pnorm(1:4) - pnorm(0:3))) > text(c((0:3)+0.5,(0:-3)-0.5), c(0.16, 0.05, 0.04, 0.02), pd, col=c("white","white","black","black")) > segments(c(-2.5, -3.5, 2.5, 3.5), dnorm(c(2.5, 3.5)), c(-2.5, -3.5, 2.5, 3.5), c(0.03, 0.01)) > >