Advanced Statistics with Applications in R

Chapter 4Four important distributions in statistics

In this chapter, we consider the four most important distributions in statistics: the multivariate normal distribution, the chi‐square distribution (‐distribution), the ‐distribution, and the ‐distribution. The multivariate normal distribution is the parent to all. These distributions are especially useful for statistical models under the most popular normal distribution assumption. Also, these distributions arise in asymptotic theory, when the sample size goes to infinity, even when the original distribution is not normal or even continuous.

It is especially convenient to work with multidimensional distributions using matrix algebra. The basics of matrix algebra are found in Section 10.2.

4.1 Multivariate normal distribution

The bivariate (two‐dimensional, ) normal distribution was introduced in Section 3.5. In this section, we study the multivariate normal distribution of an ‐dimensional random vector

Thus, it is useful to review ...