CHAPTER 6 - Some Special Absolutely Continuous Distributions

Abstract

This chapter discusses some special absolutely continuous distributions. The distribution of χ2 is called the chi-square (or χ2) distribution with n degrees of freedom. A very important property of the chi-square distribution is called the reproductive property. The two distributions—F-distribution and t-distribution—are among the most important in practical applications of mathematical statistics. To obtain the F-distribution, two independent random variables X, Y, where X has a chi-square distribution with m degrees of freedom, and Y has a chi-square distribution with n degrees of freedom is considered. The distribution of the random variable U is called the F-distribution with (m, n) degrees of freedom. A random variable has a t-distribution with n degrees of freedom if it has the same distribution function.