Preliminaries

In this chapter, we address and review key concepts that will be used in later chapters. In Sect. 1.1, we review briefly the key notions of probability functions and moments of random vectors. Then, we introduce step and impulse functions, which will prove useful in describing and analyzing non-linear statistics, in Sect. 1.2. Section 1.3 is devoted to the discussion on signs and magnitudes of random variables, which will play an important role in describing and understanding order and rank statistics. In the discussion, we will find interesting applications of the step and impulse functions. In Sect. 1.4, we introduce concisely the notions of order statistics, magnitude order statistics, ranks, and magnitude ranks of random vectors, which are the themes of the following chapters.