Recursions for convolutions and compound distributions with insurance applications: with 16 tables
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | EAA lecture notes
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 345 S. |
| ISBN: | 3540928995 9783540928997 |
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| 100 | 1 | |a Sundt, Bjørn |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Recursions for convolutions and compound distributions with insurance applications |b with 16 tables |c Bjørn Sundt ; Raluca Vernic |
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Record in the Search Index
| _version_ | 1804138535716913152 |
|---|---|
| adam_text | 2.6.3 COUNTING DISTRIBUTION WITH RANGE BOUNDED FROM ABOVE . . 55
CONTENTS PART I UNIVARIATE DISTRIBUTIONS 1 INTRODUCTION 3 . 1 AGGREGATE
CLAIMS DISTRIBUTIONS 3 .2 SOME NOTATION AND CONVENTIONS 6 .3 CLASSES OF
DISTRIBUTIONS AND FUNCTIONS 7 .4 CONVOLUTIONS 8 .5 MIXED DISTRIBUTIONS 9
1.6 COMPOUND DISTRIBUTIONS AND FUNCTIONS 11 1.7 SOME USEFUL TRANSFORMS
12 1.7.1 DEFINITIONS AND GENERAL RESULTS 12 1.7.2 CONVOLUTIONS 14 1.7.3
DISCRETE DISTRIBUTIONS 15 1.7.4 COMPOUND DISTRIBUTIONS 16 1.7.5
EXTENSION TO FUNCTIONS 17 1.8 SOME USEFUL OPERATORS 17 1.9 STOP LOSS
PREMIUMS 20 1.10 CONVERGENCE OF INFINITE SERIES WITH POSITIVE TERMS 25 2
COUNTING DISTRIBUTIONS WITH RECURSION OF ORDER ONE 29 2.1 GEOMETRIE
DISTRIBUTION 29 2.2 POISSON DISTRIBUTION 30 2.2.1 GENERAL RECURSION 30
2.2.2 APPLICATION OF GENERATING FUNCTIONS 31 2.3 THE PANJER CLASS 36
2.3.1 PANJER RECURSIONS 36 2.3.2 SUBCLASSES 39 2.3.3 AN ALTERNATIVE
RECURSION 43 2.4 CONVOLUTIONS OF A DISTRIBUTION 45 2.5 THE SUNDT-JEWELL
CLASS 48 2.5.1 CHARACTERISATION 48 2.5.2 RECURSIONS 50 2.5.3 SUBCLASSES
51 2.6 HIGHER ORDER PANJER CLASSES 54 2.6.1 CHARACTERISATION 54 2.6.2
SHIFTED COUNTING DISTRIBUTION 54 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/99214762X DIGITALISIERT DURCH CONTENTS 2.7 EXTENSION TO
SEVERITY DISTRIBUTIONS IN PIO 56 2.7.1 RECURSIONS 56 2.7.2 THINNING 58
2.7.3 CONVERSION TO SEVERITY DISTRIBUTIONS IN V I 59 COMPOUND MIXED
POISSON DISTRIBUTIONS 65 3.1 MIXED POISSON DISTRIBUTIONS 65 3.2 GAMMA
MIXING DISTRIBUTION 67 3.3 GENERAL RECURSION 68 3.4 FINITE MIXTURES 69
3.5 WILLMOT MIXING DISTRIBUTION 69 3.6 THE COUNTING DISTRIBUTION 72 3.7
INVARIANCE PROPERTIES IN THE WILLMOT CLASS 75 3.7.1 INTRODUCTION 75
3.7.2 SCALING 75 3.7.3 SHIFTING 76 3.7.4 TRUNCATING 77 3.7.5 POWER
TRANSFORM 77 3.8 SPECIAL CLASSES OF MIXING DISTRIBUTIONS 79 3.8.1
SHIFTED PARETO DISTRIBUTION 79 3.8.2 PARETO DISTRIBUTION 79 3.8.3
TRUNCATED NORMAL DISTRIBUTION 80 3.8.4 INVERSE GAUSS DISTRIBUTION 81
3.8.5 TRANSFORMED GAMMA DISTRIBUTION 82 INFINITE DIVISIBILITY 85 4.1
DEFINITIONS AND PROPERTIES 85 4.2 CHARACTERISATION 87 4.3 MIXED POISSON
DISTRIBUTIONS 89 4.3.1 INFINITELY DIVISIBLE MIXING DISTRIBUTION 89 4.3.2
MIXING DISTRIBUTION IN V O 91 4.4 DE PRIL TRANSFORMS OF INFINILELY
DIVISIBLE DISTRIBUTIONS IN V O ... 92 4.4.1 DEFINITION AND PROPERTIES 92
4.4.2 CHARACTERISATION OF INFINITELY DIVISIBLE DISTRIBUTIONS IN TERMS OF
DE PRIL TRANSFORMS 97 COUNTIN CONTENTS VII 5.3.4 CONVOLUTIONS 112 5.3.5
CUMULANTS 119 5.4 COUNTING DISTRIBUTIONS WITH RATIONAL GENERATING
FUNCTION 122 6 DE PRIL TRANSFORMS OF DISTRIBUTIONS IN PIO 127 6.1
GENERAL RESULTS 127 6.2 THE 7* CLASSES 130 7 INDIVIDUAL MODELS 135 7.1
DE PRIL S METHODS 135 7.2 DHAENE-VANDEBROEK S METHOD 137 7.3 DE PRIL S
INDIVIDUAL MODEL 138 7.4 COLLECTIVE APPROXIMATIONS 140 8 CUMULATIVE
FUNCTIONS AND TAILS 149 8.1 GENERAL RESULTS 149 8.2 CONVOLUTIONS 153 8.3
COMPOUND DISTRIBUTIONS 154 8.4 DE PRIL TRANSFORMS 155 8.5 THE SPECIAL
CASE B = 0 156 9 MOMENTS 161 9.1 CONVOLUTIONS OF A DISTRIBUTION 161
9.1.1 ORDINARY MOMENTS 161 9.1.2 THE NORMAL DISTRIBUTION 165 9.1.3
FACTORIAL MOMENTS 167 9.2 COMPOUND DISTRIBUTIONS 168 9.2.1 GENERAL
RESULTS 168 9.2.2 COMPOUND PANJER DISTRIBUTIONS 174 9.2.3 COMPOUND
POISSON DISTRIBUTIONS 178 10 APPROXIMATIONS BASED ON DE PRIL TRANSFORMS
181 10.1 INTRODUCTION 181 10.2 EXTENSIONOF RESULTS FOR DISTRIBUTIONS 183
10.2.1 KEYRESULT 183 10.2.2 APPLICATIONS 185 10.3 ERROR BOUNDS 186
10.3.1 MAINRESULT 186 10.3.2 THE DHAENE-DE PRIL TRANSFORM 189 10.3.3
COROLLARIES TO THE MAIN RESULT 190 10.3. VUEI CONTENTS 10.6 THE KORNYA
APPROXIMATION 200 10.6.1 GENERAL COUNTING DISTRIBUTION 200 10.6.2
COUNTING DISTRIBUTION IN TZ 201 10.6.3 DE PRIL S INDIVIDUAL MODEL 202
10.7 THE HIPP APPROXIMATION 204 10.7.1 GENERAL COUNTING DISTRIBUTION 204
10.7.2 BERNOULLI COUNTING DISTRIBUTION 205 10.7.3 DE PRIL S INDIVIDUAL
MODEL 208 10.8 NUMERICAL EXAMPLE 209 11 EXTENSION TO DISTRIBUTIONS IN
V _ 217 11.1 DE PRIL TRANSFORMS 217 11.1.1 DEFINITION 217 11.1.2
EXTENSION OF RESULTS 219 11.2 ERRORBOUNDS 220 12 ALLOWING FOR NEGATIVE
SEVERITIES 223 12.1 INTRODUCTION 223 12.2 BINOMIAL COUNTING DISTRIBUTION
224 12.3 POISSON COUNTING DISTRIBUTION 226 12.4 NEGATIVE BINOMIAL
COUNTING DISTRIBUTION 228 13 UNDERFLOW AND OVERFLOW 231 13.1 SIMPLE
SCALING 231 13.2 EXPONENTIAL SCALING 231 13.3 CONVOLUTIONS 233 PART II
MULTIVARIATE DISTRIBUTIONS 14 INTRODUCTION 237 14.1 AGGREGATE CLAIMS
DISTRIBUTIONS 237 14.2 VECTORS AND MATRICES 239 14.3 INDUCTION PROOFS IN
A MULTIVARIATE SETTING 240 14.4 CLASSES OF DISTRIBUTIONS AND FUNCTIONS
241 14.5 CONVOLUTIONS 241 14.6 COMPOUND DISTRIBUTIONS 242 14.7 MOMENTS
244 15 MULTIVARIATE COMPOUND DISTRIBUTIONS OF TYPE 1 24 CONTENTS IX 16
DE PRIL TRANSFORMS 259 16.1 DEFINITIONS 259 16.2 THE TZ K CLASSES 260
16.3 INFINITE DIVISIBILITY 262 16.4 EXTENSION TO FUNCTIONS IN T M $ 263
16.5 VECTORS OF INDEPENDENT RANDOM SUBVECTORS 263 16.6 VECTORS OF LINEAR
COMBINATIONS OF INDEPENDENT RANDOM VARIABLES 267 16.7 INDIVIDUAL MODELS
271 17 MOMENTS 275 17.1 CONVOLUTIONS OF A DISTRIBUTION 275 17.1.1
MOMENTS 275 17.1.2 THE MULTINORMAL DISTRIBUTION 279 17.2 COMPOUND
DISTRIBUTIONS 281 17.2.1 GENERAL RESULTS 281 17.2.2 COMPOUND PANJER
DISTRIBUTIONS 283 18 APPROXIMATIONS BASED ON DE PRIL TRANSFORMS 287 18.1
APPROXIMATIONS 287 18.2 ERRORBOUNDS 287 19 MULTIVARIATE COMPOUND
DISTRIBUTIONS OF TYPE 2 289 19.1 MAIN FRAMEWORK 289 19.2 RECURSIONS OF
HIGHER ORDER 294 19.3 MULTIVARIATE COMPOUND DISTRIBUTIONS OF TYPE 3 295
20 COMPOUND MIXED MULTIVARIATE POISSON DISTRIBUTIONS 297 20.1
MULTIVARIATE POISSON DISTRIBUTIONS 297 20.2 EXTENSION TO MIXED
DISTRIBUTIONS 300 20.3 GAMMA MIXING DISTRIBUTION 301 20.4 COMPOUND
DISTRIBUTIONS WITH UNIVARIATE COUNTING DISTRIBUTION . . 304 20.4.1
GENERAL RECURSION 304 20.4.2 WILLMOT MIXING DISTRIBUTION 305 20. X
CONTENTS REFERENCES 327 LIST OF NOTATION 337 AUTHOR INDEX 339 SUBJECT
INDEX 343
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:29:44Z |
| institution | BVB |
| isbn | 3540928995 9783540928997 |
| language | English |
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| physical | XV, 345 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | EAA lecture notes |
| spelling | Sundt, Bjørn Verfasser aut Recursions for convolutions and compound distributions with insurance applications with 16 tables Bjørn Sundt ; Raluca Vernic Berlin [u.a.] Springer 2009 XV, 345 S. txt rdacontent n rdamedia nc rdacarrier EAA lecture notes Mathematisches Modell Insurance Mathematical models Insurance Statistical methods Zusammengesetzte Verteilung (DE-588)4191153-2 gnd rswk-swf Zusammengesetzte Verteilung (DE-588)4191153-2 s DE-604 Vernic, Raluca Verfasser aut Erscheint auch als Online-Ausgabe 978-3-540-92900-0 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017060615&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sundt, Bjørn Vernic, Raluca Recursions for convolutions and compound distributions with insurance applications with 16 tables Mathematisches Modell Insurance Mathematical models Insurance Statistical methods Zusammengesetzte Verteilung (DE-588)4191153-2 gnd |
| subject_GND | (DE-588)4191153-2 |
| title | Recursions for convolutions and compound distributions with insurance applications with 16 tables |
| title_auth | Recursions for convolutions and compound distributions with insurance applications with 16 tables |
| title_exact_search | Recursions for convolutions and compound distributions with insurance applications with 16 tables |
| title_full | Recursions for convolutions and compound distributions with insurance applications with 16 tables Bjørn Sundt ; Raluca Vernic |
| title_fullStr | Recursions for convolutions and compound distributions with insurance applications with 16 tables Bjørn Sundt ; Raluca Vernic |
| title_full_unstemmed | Recursions for convolutions and compound distributions with insurance applications with 16 tables Bjørn Sundt ; Raluca Vernic |
| title_short | Recursions for convolutions and compound distributions with insurance applications |
| title_sort | recursions for convolutions and compound distributions with insurance applications with 16 tables |
| title_sub | with 16 tables |
| topic | Mathematisches Modell Insurance Mathematical models Insurance Statistical methods Zusammengesetzte Verteilung (DE-588)4191153-2 gnd |
| topic_facet | Mathematisches Modell Insurance Mathematical models Insurance Statistical methods Zusammengesetzte Verteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017060615&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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