Practical analysis of extreme values:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Leuven
Leuven Univ. Press
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 137, 33 S. graph. Darst. |
| ISBN: | 9061867681 |
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MARC
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| 245 | 1 | 0 | |a Practical analysis of extreme values |c Jan Beirlant ; Jozef L. Teugels ; Petra Vynckier |
| 264 | 1 | |a Leuven |b Leuven Univ. Press |c 1996 | |
| 300 | |a 137, 33 S. |b graph. Darst. | ||
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| 650 | 7 | |a Statistische methoden |2 gtt | |
| 650 | 7 | |a Valeurs extrêmes, Théorie des |2 ram | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Extreme value theory | |
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Record in the Search Index
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| adam_text | Contents
INTRODUCTION 1
1 AIMS AND STATISTICAL TOOLS 3
1.1 Practical examples 3
1.2 Basic assumptions and notations 5
1.3 Operations on distributions 9
1.3.1 Convolutions 9
1.3.2 Transformation 10
1.3.3 Conditioning 12
1.3.4 Truncation or censoring 13
1.3.5 Mixing 14
1.4 A working list of loss distribution models 14
1.5 Quantile plots 18
1.5.1 The exponential quantile plot 19
1.5.2 The Weibull quantile plot 24
1.5.3 The lognormal quantile plot 25
1.5.4 The Pareto quantile plot 28
1.5.5 Quantile plots in general 31
1.5.6 A case study: hurricane data 34
1.6 Excess functions 37
1.6.1 Basic properties of e 38
1.6.2 Use of empirical mean excess plots 41
1.6.3 Extensions: Hill statistics, trimmed and median excess plots . 43
1.6.4 The quadratic mean excess function 45
1.7 Bibliographical notes 47
2 PARETO TYPE MODELS 49
2.1 The domain of attraction problem for extremes 49
2.2 Regular variation, Pareto type distributions 51
2.3 Estimation of the Pareto index 55
CONTENTS
2.3.1 Consistency of the Hill estimator 55
2.3.2 The bias of the Hill estimator 56
2.3.3 Other Pareto index estimators 57
2.4 Implementation of the Hill estimator 59
2.5 Confidence intervals for the Pareto index 64
2.6 Estimation of large Pareto quantiles and return periods 66
2.7 Estimation of the Pareto index under right censoring 70
2.8 Bibliographical notes 71
3 THE EXTREME VALUE INDEX 73
3.1 The domain of attraction problem 73
3.2 Estimation of the extreme value index 7 77
3.2.1 A quantile plot approach 78
3.2.2 The adapted Hill estimator 81
3.2.3 Practical implementation of the adapted Hill estimator .... 84
3.3 Estimation of high quantiles or finite endpoints under the general
extreme value model 97
3.4 Bibliographical notes 98
4 WEIBULL TYPE DISTRIBUTIONS 99
4.1 Weibull type distributions 99
4.2 Estimation of the Weibull index r 101
4.3 Estimation of large Weibull quantiles and return periods 108
4.4 Bibliographical notes 109
5 ACTUARIAL APPLICATIONS 111
5.1 Models for the claim times process 112
5.2 The total claim amount 117
5.2.1 The normal power approximation 118
5.2.2 Subexponential claim distributions 120
5.3 Ruin probabilities 121
5.4 Solvency analysis 122
5.4.1 Excess oi loss reinsurance 124
5.5 Bibliographical notes 127
BIBLIOGRAPHY 129
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| id | DE-604.BV011337543 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:08:02Z |
| institution | BVB |
| isbn | 9061867681 |
| language | English |
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| physical | 137, 33 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Leuven Univ. Press |
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| spelling | Beirlant, Jan Verfasser (DE-588)170449963 aut Practical analysis of extreme values Jan Beirlant ; Jozef L. Teugels ; Petra Vynckier Leuven Leuven Univ. Press 1996 137, 33 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Distributions, Théorie des (analyse fonctionnelle) ram Développements asymptotiques ram Extreme waarden gtt Statistische methoden gtt Valeurs extrêmes, Théorie des ram Asymptotic expansions Extreme value theory Theory of distributions (Functional analysis) Extremwertstatistik (DE-588)4153429-3 gnd rswk-swf Extremwertstatistik (DE-588)4153429-3 s DE-604 Teugels, Jef L. Verfasser (DE-588)135849446 aut Vynckier, Petra Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007617121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beirlant, Jan Teugels, Jef L. Vynckier, Petra Practical analysis of extreme values Distributions, Théorie des (analyse fonctionnelle) ram Développements asymptotiques ram Extreme waarden gtt Statistische methoden gtt Valeurs extrêmes, Théorie des ram Asymptotic expansions Extreme value theory Theory of distributions (Functional analysis) Extremwertstatistik (DE-588)4153429-3 gnd |
| subject_GND | (DE-588)4153429-3 |
| title | Practical analysis of extreme values |
| title_auth | Practical analysis of extreme values |
| title_exact_search | Practical analysis of extreme values |
| title_full | Practical analysis of extreme values Jan Beirlant ; Jozef L. Teugels ; Petra Vynckier |
| title_fullStr | Practical analysis of extreme values Jan Beirlant ; Jozef L. Teugels ; Petra Vynckier |
| title_full_unstemmed | Practical analysis of extreme values Jan Beirlant ; Jozef L. Teugels ; Petra Vynckier |
| title_short | Practical analysis of extreme values |
| title_sort | practical analysis of extreme values |
| topic | Distributions, Théorie des (analyse fonctionnelle) ram Développements asymptotiques ram Extreme waarden gtt Statistische methoden gtt Valeurs extrêmes, Théorie des ram Asymptotic expansions Extreme value theory Theory of distributions (Functional analysis) Extremwertstatistik (DE-588)4153429-3 gnd |
| topic_facet | Distributions, Théorie des (analyse fonctionnelle) Développements asymptotiques Extreme waarden Statistische methoden Valeurs extrêmes, Théorie des Asymptotic expansions Extreme value theory Theory of distributions (Functional analysis) Extremwertstatistik |
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