CODEWITHSUNDEEP
rdistributionreverseinverse
geotheory
geotheory

Reputation: 23680

The reverse/inverse of the normal distribution function in R

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

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

enter image description here

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?

Upvotes: 17

Views: 50902

Answers (3)

Antoni Parellada
Antoni Parellada

Reputation: 4811

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

enter image description here

Upvotes: 4

gung - Reinstate Monica
gung - Reinstate Monica

Reputation: 11903

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.

Upvotes: 26

mrip
mrip

Reputation: 15163

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)

enter image description here

Upvotes: 8

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