Records : mathematical theory / Valery B. Nevzorov.

Format:

Book

Author/Creator:

Nevzorov, V. B. (Valeriĭ Borisovich), 1946-

Series:

Translations of mathematical monographs 0065-9282 ; v. 194.

Translations of mathematical monographs, 0065-9282 ; v. 194

Standardized Title:

Rekordy. English

Language:

English

Russian

Subjects (All):

Order statistics.

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