Lundberg approximations for compound distributions with insurance applications:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
|
| Series: | Lecture notes in statistics
156 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 250 S. |
| ISBN: | 0387951350 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lundberg approximations for compound distributions with insurance applications |c Gordon E. Willmot ; X. Sheldon Lin |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
2 Reliability background 7
2.1 The failure rate 8
2.2 Equilibrium distributions 14
2.3 The residual lifetime distribution and its mean 18
2.4 Other classes of distributions 24
2.5 Discrete reliability classes 28
2.6 Bounds on ratios of discrete tail probabilities 34
3 Mixed Poisson distributions 37
3.1 Tails of mixed Poisson distributions 38
3.2 The radius of convergence 40
3.3 Bounds on ratios of tail probabilities 42
3.4 Asymptotic tail behaviour of mixed Poisson distributions . 46
4 Compound distributions 51
4.1 Introduction and examples 52
4.2 The general upper bound 65
4.3 The general lower bound 73
4.4 A Wald type martingale approach 78
5 Bounds based on reliability classifications 81
5.1 First order properties 81
x Contents 1
i
5.2 Bounds based on equilibrium properties 87
6 Parametric Bounds 93
6.1 Exponential bounds 94 ;
6.2 Pareto bounds 97
6.3 Product based bounds 100
7 Compound geometric and related distributions 107
7.1 Compound modified geometric distributions 108
7.2 Discrete compound geometric distributions 114
7.3 Application to ruin probabilities 129
7.4 Compound negative binomial distributions 132
8 Tijms approximations 141
8.1 The asymptotic geometric case 141
8.2 The modified geometric distribution 147
8.3 Transform derivation of the approximation 148
9 Defective renewal equations 151
9.1 Some properties of defective renewal equations 152
9.2 The time of ruin and related quantities 159
9.3 Convolutions involving compound geometric distributions . 174
10 The severity of ruin 183
10.1 The associated defective renewal equation 183
10.2 A mixture representation for the conditional distribution . . 186
10.3 Erlang mixtures with the same scale parameter 192
10.4 General Erlang mixtures 198
10.5 Further results 205
11 Renewal risk processes 209
11.1 General properties of the model 210
11.2 The Coxian 2 case 216
11.3 The sum of two exponentials 224
11.4 Delayed and equilibrium renewal risk processes 226
Bibliography 235
Symbol Index 243
Author Index 245
Subject Index 248
|
| any_adam_object | 1 |
| author | Willmot, Gordon E. 1957- Lin, X. Sheldon |
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| id | DE-604.BV013475845 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:30Z |
| institution | BVB |
| isbn | 0387951350 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009196439 |
| oclc_num | 44727700 |
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| physical | X, 250 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Willmot, Gordon E. 1957- Verfasser (DE-588)122585860 aut Lundberg approximations for compound distributions with insurance applications Gordon E. Willmot ; X. Sheldon Lin New York [u.a.] Springer 2001 X, 250 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 156 Assurance - Méthodes statistiques Assurance - Méthodes statistiques ram Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Risicoanalyse gtt Statistische modellen gtt Verdelingen (statistiek) gtt Verzekeringswiskunde gtt Distribution (Probability theory) Insurance Statistical methods Zusammengesetzte Verteilung (DE-588)4191153-2 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Zusammengesetzte Verteilung (DE-588)4191153-2 s Approximation (DE-588)4002498-2 s DE-604 Lin, X. Sheldon Verfasser (DE-588)171700473 aut Lecture notes in statistics 156 (DE-604)BV002447846 156 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009196439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Willmot, Gordon E. 1957- Lin, X. Sheldon Lundberg approximations for compound distributions with insurance applications Lecture notes in statistics Assurance - Méthodes statistiques Assurance - Méthodes statistiques ram Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Risicoanalyse gtt Statistische modellen gtt Verdelingen (statistiek) gtt Verzekeringswiskunde gtt Distribution (Probability theory) Insurance Statistical methods Zusammengesetzte Verteilung (DE-588)4191153-2 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4191153-2 (DE-588)4002498-2 |
| title | Lundberg approximations for compound distributions with insurance applications |
| title_auth | Lundberg approximations for compound distributions with insurance applications |
| title_exact_search | Lundberg approximations for compound distributions with insurance applications |
| title_full | Lundberg approximations for compound distributions with insurance applications Gordon E. Willmot ; X. Sheldon Lin |
| title_fullStr | Lundberg approximations for compound distributions with insurance applications Gordon E. Willmot ; X. Sheldon Lin |
| title_full_unstemmed | Lundberg approximations for compound distributions with insurance applications Gordon E. Willmot ; X. Sheldon Lin |
| title_short | Lundberg approximations for compound distributions with insurance applications |
| title_sort | lundberg approximations for compound distributions with insurance applications |
| topic | Assurance - Méthodes statistiques Assurance - Méthodes statistiques ram Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Risicoanalyse gtt Statistische modellen gtt Verdelingen (statistiek) gtt Verzekeringswiskunde gtt Distribution (Probability theory) Insurance Statistical methods Zusammengesetzte Verteilung (DE-588)4191153-2 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Assurance - Méthodes statistiques Distribution (Théorie des probabilités) Distribution (théorie des probabilités) Risicoanalyse Statistische modellen Verdelingen (statistiek) Verzekeringswiskunde Distribution (Probability theory) Insurance Statistical methods Zusammengesetzte Verteilung Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009196439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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