The reverse/inverse of the normal distribution function in R

Question

To plot a normal distribution curve in R we can use:

(x = seq(-4,4, length=100))
y = dnorm(x)
plot(x, y)

If dnorm calculates y as a function of x, does R have a function that calculates x as a function of y? If not what is the best way to approach this?

Answer 1

I'm not sure if the inverse of the density function is built in -- it's not used nearly as often as the inverse of the cumulative distribution function. I can't think offhand of too many situation where the inverse density function is useful. Of course, that doesn't mean there aren't any, so if you are sure this is the function you need, you could just do:

dnorminv<-function(y) sqrt(-2*log(sqrt(2*pi)*y))

plot(x, y)
points(dnorminv(y),y,pch=3)

Answer 2

What dnorm() is doing is giving you a probability density function. If you integrate over that, you would have a cumulative distribution function (which is given by pnorm() in R). The inverse of the CDF is given by qnorm(); that is the standard way these things are conceptualized in statistics.

Answer 3

The derivation of the inverse of the standard normal pdf is: