1. Introduction
In this slecture, we will explain the principle of how to generate Gaussian random samples. Even though there are more general methods to generate random samples which have any distribution, we will focus on the simple method such as Box Muller transform to generate Gaussian random samples in this slecture. To do this, we will introduce inverse transform sampling which is a bas method for pseudo random number sampling first. Then, we will explain Gaussian random sample generation method based on Box Muller transform. Finally, we will introduce Marsaglia polar method which improves Box Muller transform.
2. Inverse transform sampling
Let U be a random variable which is uniformly distributed on the interval [0, 1]. And let F be a continuous CDF(cumulative distribution function). Then, inverse CDF is defined by
