Generating Simulated Data Points That Follow a Given Probability Density Function

During the last couple of weeks, I’ve been simulating some data for a statistical inference project. While the topic of simulating data is quite broad and depends on the application, I thought that a more general approach of simulating data points that follow a particular probability distribution may be useful to those working on scientific experiments and mathematical modeling.

This post combines a few basic techniques in order to generate some simulated data that follow the distribution of a given probability density function (p.d.f).

Let’s assume that we have a p.d.f of the form,

Plotting this to verify,

The choice of function is arbitrary, I’m using a Gaussian p.d.f here for simplicity/as a toy problem.