Overview
- Examples, exercises & supplements are included
- Highlights the extremal properties of combinatorial configurations obtained by using probabilistic methods
- Presents results related to extreme values in time series with missing observations
Part of the book series: Springer Series in Operations Research and Financial Engineering (ORFE)
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Keywords
- Extreme values
- Stationary sequences
- Regular variation
- Missing observations
- Probabilistic methods in Combinatorics
About this book
The main subject is the probabilistic extreme value theory. The purpose is to present recent results related to limiting distributions of maxima in incomplete samples from stationary sequences, and results related to extremal properties of different combinatorial configurations. The necessary contents related to regularly varying functions and basic results of extreme value theory are included in the first two chapters with examples, exercises and supplements. The motivation for consideration maxima in incomplete samples arises from the fact that real data are often incomplete. A sequence of observed random variables from a stationary sequence is also stationary only in very special cases. Hence, the results provided in the third chapter are also related to non-stationary sequences. The proof of theorems related to joint limiting distribution of maxima in complete and incomplete samples requires a non-trivial combination of combinatorics and point process theory. Chapter four provides results on the asymptotic behavior of the extremal characteristics of random permutations, the coupon collector's problem, the polynomial scheme, random trees and random forests, random partitions of finite sets, and the geometric properties of samples of random vectors. The topics presented here provide insight into the natural connections between probability theory and algebra, combinatorics, graph theory and combinatorial geometry.
The contents of the book may be useful for graduate students and researchers who are interested in probabilistic extreme value theory and its applications.
Authors and Affiliations
Bibliographic Information
Book Title: Extreme Values In Random Sequences
Authors: Pavle Mladenović
Series Title: Springer Series in Operations Research and Financial Engineering
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-57411-5Due: 11 June 2024
Softcover ISBN: 978-3-031-57414-6Due: 11 June 2024
eBook ISBN: 978-3-031-57412-2Due: 11 June 2024
Series ISSN: 1431-8598
Series E-ISSN: 2197-1773
Edition Number: 1
Number of Pages: XII, 278
Number of Illustrations: 3 b/w illustrations