Sampling from Known Distributions

In this chapter, we give an overview of different methods that can be used to generate random variates from a given distribution. Even if inversion should be the preferred choice for quasi–Monte Carlo users, it is important to be aware of other methods that are available for that purpose. First of all, inversion is sometimes slower and more difficult to apply than other methods. In such cases, Monte Carlo users may prefer these other methods. Also, when working with predefined functions (e.g., randn in Matlab) to generate observations from a given distribution, it is quite possible that the underlying method is not based on inversion. In addition, there are applications for which the common approach used by people working in that area is to use something other than inversion (e.g., in computer graphics, for ray generation). In such cases, even if ultimately the quasi–Monte Carlo user will try to use inversion instead of these other methods in order to modify code or algorithms appropriately, it is important to understand what the other method does. Finally, in some cases inversion may not be directly applicable, and an alternative method needs to be used.