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Preliminaries

In: Fundamentals of Order and Rank Statistics

Author

Listed:
  • Iickho Song

    (Korea Advanced Institute of Science and Technology (KAIST), School of Electrical Engineering)

  • So Ryoung Park

    (The Catholic University of Korea, School of Information, Communications, and Electronics Engineering)

  • Wenyi Zhang

    (University of Science and Technology of China, School of Information Science and Technology)

  • Seungwon Lee

    (Samsung Electronics, Modem Development Team)

Abstract

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.

Suggested Citation

  • Iickho Song & So Ryoung Park & Wenyi Zhang & Seungwon Lee, 2024. "Preliminaries," Springer Books, in: Fundamentals of Order and Rank Statistics, chapter 0, pages 1-80, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-50601-7_1
    DOI: 10.1007/978-3-031-50601-7_1
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