Pretty Normal

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))