Simulating generative distributions

We have seen that we can draw random numbers out of distributions for which we have a convenient transform or access to a quantile function. We have also seen that we can derive a probability mass function or probability density function from the story of a distribution, and those PMFs/PDFs give us complete information about the distribution. Sometimes, though, it is difficult or impossible to derive a PMF or PDF from a story. In other situations, we may know the PMF or PDF buy cannot derive a transform nor an easily evaluated quantile function. In these cases, we can simulate the story of the distribution using random number generation.

In this section, we will learn how to simulate distributions through three examples, the Luria-Delbrück distribution from their famous experiment, the noisy integrate-and-fire model of neurons, and nonhomogenous Poisson processes as a model for neuronal spiking.