Introduction to Stochastic Processes and Simulation

8Generator Programs

CONCEPTS DISCUSSED IN THIS CHAPTER.– The practice of simulation must generate random events, which results in the generation of random numbers. These random numbers can obey various laws, laws known as the usual distributions discussed in Chapter 2, or any laws.

This chapter is devoted first to the technique of generating random numbers for the usual distributions, then for any probability law.

The case where any law can be replaced by a usual distribution is the subject of the presentation of the χ2 compliance test.

Recommended reading: [PHE 77].

8.1. Random and pseudo-random numbers

A number is random if it is chosen at random, but obeying a known or unknown law of probability. The simplest of these laws is the uniform distribution. We will begin by studying the problem of the generation of random numbers according to the uniform distribution. We will see that other laws can be simulated from this distribution.

But how are random numbers according to the uniform distribution generated? The first answers come from the observation of physical phenomena, the simplest being drawn from games called “games of chance”, such as throwing a die (perfect) or the result of roulette (also perfect). What is more sophisticated is the generation of random numbers from electrical noise, which is impossible to predict from electronic circuits.

The use of roulette, simulated by an electronic mechanism, is at the origin of the RAND Corporation’s famous table in the 1940s. ...