An introduction to heavy-tailed and subexponential distributions:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Heidelberg ; Dordrecht ; London
Springer
[2013]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Springer series in operations research and financial engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 157 Seiten Diagramme |
| ISBN: | 9781461471004 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to heavy-tailed and subexponential distributions |c Sergey Foss, Dmitry Korshunov, Stan Zachary |
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Datensatz im Suchindex
| _version_ | 1804150442573168640 |
|---|---|
| adam_text | Titel: An introduction to heavy-tailed and subexponential distributions
Autor: Foss, Sergey
Jahr: 2013
Contents
1 Introduction......................................................................................................1
2 Heavy-Tailed and Long-Tailed Distributions............................................7
2.1 Heavy-Tailed Distributions......................................................................7
2.2 Characterisation of Heavy-Tailed Distributions
in Terms of Generalised Moments..........................................................11
2.3 Lower Limit for Tails of Convolutions..................................................14
2.4 Long-Tailed Functions and Their Properties........................................17
2.5 Long-Tailed Distributions........................................................................21
2.6 Long-Tailed Distributions and Integrated Tails....................................22
2.7 Convolutions of Long-Tailed Distributions..........................................24
2.8 A-Insensitive Distributions......................................................................31
2.9 Comments................................................................................................38
2.10 Problems..................................................................................................39
3 Subexponential Distributions........................................................................43
3.1 Subexponential Distributions on the Positive Half-Line......................43
3.2 Subexponential Distributions on the Whole Real Line........................45
3.3 Subexponentiality and Weak Tail-Equivalence....................................49
3.4 The Class S* of Strong Subexponential Distributions..........................53
3.5 Sufficient Conditions for Subexponentiality..........................................57
3.6 Conditions for Subexponentiality in Terms
of Truncated Exponential Moments......................................................59
3.7 S Is a Proper Subset of £........................................................................62
3.8 Does F e S Imply That F¡ e S?..............................................................63
3.9 Closure Properties of the Class of Subexponential Distributions________65
3.10 Kesten s Bound........................................................................................67
3.11 Subexponentiality and Randomly Stopped Sums................................69
3.12 Comments................................................................................................71
3.13 Problems ..................................................................................................72
ix
X Contents
4 Densities and Local Probabilities................................. 75
4.1 Long Tailed Densities and Their Convolutions.................. 75
4.2 Subexponential Densities on the Positive Half-Line.............. 79
4.3 Subexponential Densities on the Real Line..................... 83
4.4 Sufficient Conditions for Subexponentiality of Densities.......... 85
4.5 A-Long-Tailed Distributions and Their Convolutions............. 86
4.6 4-Subexponcntial Distributions............................... 89
4.7 4-Subexponential Distributions on the Real Line................ 95
4.8 Sufficient Conditions for A-Subexponentiality.................. 95
4.9 Local Asymptotics for a Randomly Stopped Sum................ 97
4.10 Local Subexponentiality of Integrated Tails.....................100
4.11 Comments................................................100
4.12 Problems .................................................101
5 Maximum of Random Walk.....................................103
5.1 Asymptotics for the Maximum of a Random Walk
with a Negative Drift........................................104
5.2 Finite Time Horizon Asymptotics.............................108
5.3 Ladder Structure of Maximum of Random Walk.................113
5.4 Taboo Renewal Measures....................................114
5.5 Asymptotics for the First Ascending Ladder Height..............117
5.6 Tail of the Maximum Revisited...............................120
5.7 Local Probabilities of the Maximum...........................121
5.8 Density of the Maximum....................................122
5.9 Explicitly Calculable Ascending Ladder Heights................123
5.10 Single Server Queueing System...............................128
5.11 Ruin Probabilities in Cramér-Lundberg Model..................130
5.12 Subcriticai Branching Processes..............................133
5.13 How Do Large Values of M Occur in Standard Cases?............136
5.14 Comments................................................140
5.15 Problems.................................................141
Answers to Problems...............................................145
References.........................................................151
Index.............................................................155
|
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| author | Foss, Sergey Koršunov, Dmitrij A. Zachary, Stan |
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| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| indexdate | 2024-07-10T00:38:59Z |
| institution | BVB |
| isbn | 9781461471004 |
| language | English |
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| spelling | Foss, Sergey Verfasser (DE-588)1097617440 aut An introduction to heavy-tailed and subexponential distributions Sergey Foss, Dmitry Korshunov, Stan Zachary Second edition New York ; Heidelberg ; Dordrecht ; London Springer [2013] © 2013 xi, 157 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer series in operations research and financial engineering Mathematik Statistik Wirtschaft Distribution (Probability theory) Economics / Statistics Mathematics Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Subexponentielle Verteilung (DE-588)4202696-9 gnd rswk-swf Subexponentielle Verteilung (DE-588)4202696-9 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s 1\p DE-604 Koršunov, Dmitrij A. Verfasser aut Zachary, Stan Verfasser (DE-588)170562441 aut Erscheint auch als Online-Ausgabe 978-1-4614-7101-1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026051696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Foss, Sergey Koršunov, Dmitrij A. Zachary, Stan An introduction to heavy-tailed and subexponential distributions Mathematik Statistik Wirtschaft Distribution (Probability theory) Economics / Statistics Mathematics Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Subexponentielle Verteilung (DE-588)4202696-9 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4202696-9 |
| title | An introduction to heavy-tailed and subexponential distributions |
| title_auth | An introduction to heavy-tailed and subexponential distributions |
| title_exact_search | An introduction to heavy-tailed and subexponential distributions |
| title_full | An introduction to heavy-tailed and subexponential distributions Sergey Foss, Dmitry Korshunov, Stan Zachary |
| title_fullStr | An introduction to heavy-tailed and subexponential distributions Sergey Foss, Dmitry Korshunov, Stan Zachary |
| title_full_unstemmed | An introduction to heavy-tailed and subexponential distributions Sergey Foss, Dmitry Korshunov, Stan Zachary |
| title_short | An introduction to heavy-tailed and subexponential distributions |
| title_sort | an introduction to heavy tailed and subexponential distributions |
| topic | Mathematik Statistik Wirtschaft Distribution (Probability theory) Economics / Statistics Mathematics Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Subexponentielle Verteilung (DE-588)4202696-9 gnd |
| topic_facet | Mathematik Statistik Wirtschaft Distribution (Probability theory) Economics / Statistics Mathematics Wahrscheinlichkeitsverteilung Subexponentielle Verteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026051696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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