Chapter 4 : Generating Random Variables

Many of the methods in computational statistics require the ability to generate random variables from known probability distributions. This is at the heart of Monte Carlo simulation for statistical inference (Chapter 6), bootstrap and resampling methods (Chapters 6 and 7), Markov chain Monte Carlo techniques (Chapter 11), and the analysis of spatial point processes (Chapter 12). In addition, we use simulated random variables to explain many other topics in this book, such as exploratory data analysis (Chapter 5), density estimation (Chapter 8), and statistical pattern recognition (Chapter 9). There are many excellent books available that discuss techniques for generating random variables and the underlying theory; references will be provided in the last section. Our purpose in covering this topic is to give the reader the tools they need to generate the types of random variables that often arise in practice and to provide examples illustrating the methods. We first discuss general techniques for generating random variables, such as the inverse transformation and acceptance-rejection methods. We then provide algorithms and MATLAB code for generating random variables for some useful distributions.