How to use polygon() to shade below a probability density curve

Question

I'm having trouble getting polygon() to shade below the distribution all the way to the x-axis. It seems to shade above the exponential distribution to a y=-x line. Here is where what I have so far:

x <- seq(0,50,0.01)
y <- dexp(seq(0,50,0.01),rate=0.11)
plot(x, y, type="l", col=col2rgb("yellow",0.5), xaxs="i", yaxs="i", ylim=c(0,0.15))
polygon(x, y ,border=NA,col=col2rgb("yellow",0.5))

Thanks so much!

Answer 1

Solution is simple, by adding (0,0) to the vertices of the polygon. See below:

x <- seq(0,50,0.01)
y <- dexp(seq(0,50,0.01),rate=0.11)
plot(x, y, type="l", col=col2rgb("yellow",0.5), xaxs="i", yaxs="i", ylim=c(0,0.15))
polygon(c(0, x), c(0, y), border=NA, col=col2rgb("yellow",0.5))

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How polygon() works

polygon() will line up all vertices in order. The problem of your original code is that the origin (0, 0) is not one of the vertices, so it will not be part of the polygon. You can also consider the following toy example:

x0 <- c(0, 0.5, 1.5)
y0 <- c(1.5, 0.5, 0)
## triangle, with three vertices
plot(x0, y0, pch = ".")
polygon(x0, y0, col = "red", border = NA)
## area under triangle, four vertices
polygon(c(0, x0), c(0, y0), col = "yellow", border = NA)