A Course in Statistics with R

Chapter 6Probability and Sampling Distributions

Package(s): scatterplot3d, mvtnorm, VGAM

6.1 Introduction

In this chapter the focus will be two-fold. First, we will introduce and discuss common probability models in detail. This will cover probability models for univariate random variables, first including both discrete and continuous random variables. Apart from the associated probability measures, we will consider the cumulative probability distribution function, characteristics functions, and moment generating functions (when they exist). Sections 6.2 and 6.3 will cover some of the frequently arising probability models. Section 6.4 will deal with multivariate probability distributions of both discrete as well as continuous random vectors. A comprehensive listing source for probability distributions using R may be found at http://cran.r-project.org/web/views/Distributions.html.

The second purpose of this chapter is to show a different side of the probability models. The probability models which govern the uncertain phenomena discussed thus far implicitly assume that the parameters are known, or another way of their use is to obtain probabilities and not to be too concerned about the unknown parameters. In the real world, the parameters of probability models are not completely known and we infer their values which render the usefulness of these models. The statistical inference aspect of this problem is covered through Chapters 7 to 9. The bridge between probability models ...