Calculating the overlap of two normal distributions using monte carlo intergration

Abstract

I read this post over at the blog Cartesian Faith about Probability and Monte Carlo methods. The post describe how to numerically intregate using Monte Carlo methods. I thought the results looked cool so I used the method to calculate the overlap of two normal distributions that are separated by a Cohen’s d of 0.8. You should head over to the original post if you want a more detailed explanation of the method. And I should add that this is not the most efficient way to calculate the overlap of two gaussian distributions, but it is a fun and pretty intuitive way, plus you can make a cool plot of the result. However, I also show how to get the overlap using the cumulative distribution function and using R’s built-in integration function.