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Records : mathematical theory / Valery B. Nevzorov.

Math/Physics/Astronomy Library QA278.7 .N48 2001
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LIBRA 510.8 T687 v.1-14
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Physical Description:
x, 164 pages : illustrations ; 27 cm.
Place of Publication:
Providence, RI : American Mathematical Society, [2001]
Contents:
  • Part 1. Order Statistics 5
  • Lecture 2. Order Statistics and Their Distributions 5
  • Lecture 3. Three Classical Representations for Order Statistics 10
  • Lecture 4. Markov Property and Conditional Independence of Order Statistics 15
  • Lecture 5. Order Statistics for Nonstationary Sequences 18
  • Lecture 6. Moments of Order Statistics 21
  • Lecture 7. Moments of Order Statistics (continued) 26
  • Lecture 8. Asymptotic Distributions of the Middle Order Statistics 32
  • Lecture 9. Asymptotic Distributions of the Middle Order Statistics (continued) 38
  • Lecture 10. Asymptotic Distributions of Maxima 42
  • Lecture 11. Domains of Attraction of the Limiting Distributions of Extremes 47
  • Lecture 12. Some Topics Related to the Distribution of Extremes 50
  • Part 2. Record Times and Record Values 55
  • Lecture 13. Maxima and Records 55
  • Lecture 14. Distributions of Record Times 59
  • Lecture 15. Distributions of Record Values 65
  • Lecture 16. Shorrock's Representation for Discrete Records 69
  • Lecture 17. Joint Distributions of Record Times and Record Values 76
  • Lecture 18. Asymptotic Distributions of Record Values 79
  • Lecture 19. The kth Records 82
  • Lecture 20. Generating Function of the kth Record Times 86
  • Lecture 21. Moment Characteristics of the kth Record Times 89
  • Lecture 22. Tata's Representation and Its Generalizations 92
  • Lecture 23. Correlation Coefficients for Records 95
  • Lecture 24. Records for Nonstationary Sequences of Random Variables 101
  • Lecture 25. Record Times in the F[superscript alpha]-Scheme 107
  • Lecture 26. Independence of Record Indicators and Maxima 114
  • Lecture 27. Asymptotic Distribution of Record Values in the F[superscript alpha]-Scheme 116
  • Lecture 28. Records in Sequences of Dependent Random Variables 119
  • Lecture 29. Records and the Secretary Problem 125
  • Lecture 30. Statistical Procedures Related to Records 129
  • Appendix 1. Theory of Records: Historical Review 133
  • Appendix 2. Hints, Solutions, and Answers 137.
Notes:
Includes bibliographical references (pages 153-164).
ISBN:
0821819453
OCLC:
44727683

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