Normal Distribution Functions in R

I always need to look up how to use the distributional functions in R. Rather than it always being a guessing game I made a quick primer with visual example plots of what each command means and the results each command actually returns.

The below examples assume a N(0,1). A link to the R manual is here.

dnorm-returns the height of the normal curve at a specified value along the x-axis

pnorm-the cumulative density function (CDF) that returns the area to the left of a specified value

qnorm-returns quantiles or "critical values"

rnorm-generates random numbers from the normal distribution

These are examples for the normal distribution, but as you could imagine R has commands for numerous other distributions such as the chi-square, beta, uniform, and poisson.

If you are curious, here are the commands I used to plot these figures:

	normal <- rnorm(10000000)
	d_normal <- density(normal)
	# dnorm
	plot(d_normal, main="dnorm(1.5)", xlab="", xaxs="i", yaxs="i", xlim=c(-4.5,4.5), ylim=c(0,0.43))
	abline(h=0, col="black")
	arrows(x0=1.5,x1=1.5,y0=0,y1=dnorm(1.5), angle=0, length=0.1, lty=3)
	points(1.5, dnorm(1.5), pch=19, col="gray")
	text(1.5, dnorm(1.5), labels=paste("height=",round(dnorm(1.5),4)), pos=4)
	# pnorm
	plot(d_normal, main="pnorm(1.5)", xlab="", xaxs="i", yaxs="i", xlim=c(-4.5,4.5), ylim=c(0,0.43))
	abline(h=0, col="black")
	x3 <- 1
	x4 <- max(which(d_normal$x < 1.5))
	with(d_normal, polygon(x=c(x[c(x3,x3:x4,x4)]), y= c(0,y[x3:x4],0), col="gray"))
	text(-1, dnorm(1.2), labels=paste("area=",round(pnorm(1.5),4)), pos=4)
	# qnorm
	plot(d_normal, main="qnorm(0.9332)", xlab="", xaxs="i", yaxs="i", xlim=c(-4.5,4.5), ylim=c(0,0.43))
	abline(h=0, col="black")
	arrows(x0=1.5,x1=1.5,y0=0,y1=dnorm(1.5), angle=0, length=0.1, col="gray", lwd=2)
	text(1.5, dnorm(1.5)/2, labels=paste("cutoff value=",round(qnorm(0.9332),4)), pos=4)
	# rnorm
	plot(d_normal, main="rnorm(500)", xlab="", xaxs="i", yaxs="i", xlim=c(-4.5,4.5), ylim=c(0,0.43))
	x <- rnorm(500)
	o <- runif(500)
	y <- dnorm(x)*o
	points(x,y, pch=19, col="gray")
	abline(h=0, col="black")

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