A Course in Statistics with R

Chapter 11Monte Carlo Computations

Package(s): plotrix, LearnBayes, ConvergenceConcepts

11.1 Introduction

Simulation of observations from random experiments has always been of profound interest. Generation of random numbers has always been crucial for statisticians, both for theory and applications. The emergence of the computer and its speed has greatly benefited from the endurance of random numbers. The truth is that machines cannot really produce random numbers in the sense that the generated sequence will eventually repeat itself identically, which is more formally called the cycle of the generator. However, this does not restrict their usage for most practical situations if the required random numbers are less than the cycle of the generator. See also the important page: http://www.cran.r-project.org/web/views/Distributions.html

The current chapter unfolds along the following lines. Section 11.2 discusses how random numbers may be simulated using random generators. Three different techniques are developed here and a pressing case is made for the use of the linear congruential generator. A different way of dealing with these random numbers will be that such numbers may be treated to follow the uniform distribution . The standard uniform distribution forms the base of most simulation techniques. Using the techniques described here, some very interesting probability problems ...