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Extreme values in random sequences

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Extreme values in random sequences/ by Pavle Mladenović.
作者:	Mladenović, Pavle.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xii, 278 p. :ill., digital ;24 cm.
內容註:	Preface -- Regularly Varying Functions -- Basic Results of Extreme Value Theory -- Time Series and Missing Observations -- Combinatorial Problems and Extreme Values -- Bibliography -- Index.
Contained By:	Springer Nature eBook
標題:	Extreme value theory. -
電子資源:	https://doi.org/10.1007/978-3-031-57412-2
ISBN:	9783031574122

Extreme values in random sequences
Mladenović, Pavle.

Extreme values in random sequences[electronic resource] /by Pavle Mladenović. - Cham :Springer Nature Switzerland :2024. - xii, 278 p. :ill., digital ;24 cm. - Springer series in operations research and financial engineering,2197-1773. - Springer series in operations research and financial engineering..

Preface -- Regularly Varying Functions -- Basic Results of Extreme Value Theory -- Time Series and Missing Observations -- Combinatorial Problems and Extreme Values -- Bibliography -- Index.

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.

ISBN: 9783031574122

Standard No.: 10.1007/978-3-031-57412-2doiSubjects--Topical Terms:

646412
Extreme value theory.

LC Class. No.: QA273.6

Dewey Class. No.: 519.24

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520 $a 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.
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