calculate area of overlapping density plot by ggplot using R

Question

How can I get the area under overlapping density curves?

How can I solve the problem with R? (There is a solution for python here: Calculate overlap area of two func

Answer 1

I was looking for a way to do this for empirical data, and had the problem of multiple intersections as mentioned by user5878028. After some digging I found a very simple solution, even for a total R noob like me:

Install and load the libraries "overlapping" (which performs the calculation) and "lattice" (which displays the result):

library(overlapping)
library(lattice)

Then define a variable "x" as a list that contains the two density distributions you want to compare. For this example, the two datasets "data1" and "data2" are both columns in a text file called "yourfile":

x <- list(X1=yourfile$data1, X2=yourfile$data2)

Then just tell it to display the output as a plot which will also display the estimated % overlap:

out <- overlap(x, plot=TRUE)

I hope this helps someone like it helped me! Here's an example overlap plot

Answer 2

I will make a few base R plots, but the plots are not actually part of the solution. They are just there to confirm that I am getting the right answer.

You can get each of the density functions and solve for where they intersect.

##  Create the two density functions and display
FDensity = approxfun(density(df$weight[df$sex=="F"], from=40, to=80))
MDensity = approxfun(density(df$weight[df$sex=="M"], from=40, to=80))
plot(FDensity, xlim=c(40,80), ylab="Density")
curve(MDensity, add=TRUE)

Now solve for the intersection

## Solve for the intersection and plot to confirm
FminusM = function(x) { FDensity(x) - MDensity(x) }
Intersect = uniroot(FminusM, c(40, 80))$root
points(Intersect, FDensity(Intersect), pch=20, col="red")

Now we can just integrate to get the area of the overlap.

integrate(MDensity, 40,Intersect)$value + 
    integrate(FDensity, Intersect, 80)$value
[1] 0.2952838