Four important distributions in statistics

This chapter considers the four most important distributions in statistics: the multivariate normal distribution, the chi-square distribution, the t-distribution, and the F-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. The chi-square distribution is the distribution of the sum of squared independent standard normal random variables. The t-distribution (sometimes called the central t-distribution) is the distribution of the ratio of a standard normal variable to the square root of the independent chi-square variable divided by its df. The F-distribution, after Ronald Fisher who discovered this distribution, is the distribution of the ratio of two independent chi-square distributions divided by the corresponding df. In words, the F-distribution with the first df being one is the squared t-distribution.