Generalized linear models for insurance data:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo ; Delhi
Cambridge University Press
2008
|
| Ausgabe: | frist published |
| Schriftenreihe: | International series on actuarial science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | x, 196 Seiten Illustrationen, Diagramme |
| ISBN: | 9780521879149 |
Internformat
MARC
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| 020 | |a 9780521879149 |c (hbk.) : £35.00 hbk. : £35.00 : CIP entry (Feb.) |9 978-0-521-87914-9 | ||
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| 100 | 1 | |a De Jong, Piet |0 (DE-588)170151522 |4 aut | |
| 245 | 1 | 0 | |a Generalized linear models for insurance data |c Piet de Jong ; Department of Actuarial Studies, Macquarie University, Sydney ; Gillian Z. Heller ; Department of Statistics, Macquarie University, Sydney |
| 250 | |a frist published | ||
| 264 | 1 | |a Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo ; Delhi |b Cambridge University Press |c 2008 | |
| 300 | |a x, 196 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a International series on actuarial science | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Insurance / Mathematics | |
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 0 | 7 | |a Verallgemeinertes lineares Modell |0 (DE-588)4124382-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Versicherungsmathematik |0 (DE-588)4063194-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Versicherungsmathematik |0 (DE-588)4063194-1 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016524214 | ||
Datensatz im Suchindex
| _version_ | 1804137693099065344 |
|---|---|
| adam_text | Contents
Preface
1
■J
page
ix
Insurance
data
1
1.1
Introduction
2
1.2
Types of variables
3
1.3
Data transformations
4
1.4
Data exploration
6
1.5
Grouping and runoff triangles
10
1.6
Assessing distributions
12
1.7
Data issues and biases
13
1.8
Data sets used
14
1.9
Outline of rest of book
19
Response distributions
20
2.1
Discrete and continuous random variables
20
2.2
Bernoulli
21
2.3
Binomial
22
2.4
Poisson
23
2.5
Negative binomial
24
2.6
Normal
26
2.7
Chi-square and gamma
27
2.8
Inverse Gaussian
29
2.9
Overdispersion
30
Exercises
33
Exponential family responses and estimation
35
3.1
Exponential family
35
3.2
The variance function
36
3.3
Proof of the mean and variance expressions
37
3.4
Standard distributions in the exponential family form
37
3.5
Fitting probability functions to data
39
Exercises
41
vi
Contents
4
Linear
modeling
42
4.1
History and terminology of linear modeling
42
4.2
What does linear in linear model mean?
43
4.3
Simple linear modeling
43
4.4
Multiple linear modeling
44
4.5
The classical linear model
46
4.6
Least squares properties under the classical linear model
47
4.7
Weighted least squares
47
4.8
Grouped and ungrouped data
48
4.9
Transformations to normality and linearity
49
4.10
Categorical explanatory variables
51
4.11
Polynomial regression
53
4.12
Banding continuous explanatory variables
54
4.13
Interaction
55
4.14
Collinearity
55
4.15
Hypothesis testing
56
4.16
Checks using the residuals
58
4.17
Checking explanatory variable specifications
60
4.18
Outliers
61
4.19
Model selection
62
5
Generalized linear models
64
5.1
The generalized linear model
64
5.2
Steps in generalized linear modeling
65
5.3
Links and canonical links
66
5.4
Offsets
66
5.5
Maximum likelihood estimation
67
5.6
Confidence intervals and prediction
70
5.7
Assessing fits and the deviance
71
5.8
Testing the significance of explanatory variables
74
5.9
Residuals
77
5.10
Further diagnostic tools
79
5.11
Model selection
80
Exercises
80
6
Models for count data
81
6.1
Poisson
regression
81
6.2
Poisson overdispersion
and negative binomial regression
89
6.3
Quasi-likelihood
94
6.4
Counts and frequencies
96
Exercises
96
7
Categorical responses
97
7.1
Binary responses
97
7.2
Logistic regression
98
Contents
vii
7.3 Application
of logistic regression to vehicle insurance
99
7.4
Correcting for exposure
102
7.5
Grouped binary data
105
7.6
Goodness of fit for logistic regression
107
7.7
Categorical responses with more than two categories
110
7.8
Ordinal responses 111
7.9
Nominal responses
116
Exercises
119
8
Continuous responses
120
8.1
Gamma regression
120
8.2
Inverse Gaussian regression
125
8.3
Tweedie regression
127
Exercises
128
9
Correlated data
129
9.1
Random effects
131
9.2
Specification of within-cluster correlation
136
9.3
Generalized estimating equations
137
Exercise
140
10
Extensions to the generalized linear model
141
10.1
Generalized additive models
141
10.2
Double generalized linear models
143
10.3
Generalized additive models for location, scale and shape
143
10.4
Zero-adjusted inverse Gaussian regression
145
10.5
A mean and dispersion model for total claim size
148
Exercises
149
Appendix
1
Computer code and output
150
ALI
Poisson
regression
150
Al.
2
Negative binomial regression
156
A
1.3
Quasi-likelihood regression
159
A
1.4
Logistic regression
160
Al.
5
Ordinal regression
169
Al.
6
Nominal regression
175
Al.
7
Gamma regression
178
A
1.8
Inverse Gaussian regression
181
A
1.9
Logistic regression GLMM
183
ALIO
Logistic regression GEE
185
ALII Logistic regression GAM
187
A1.12GAMLSS
189
Al.
13
Zero-adjusted inverse Gaussian regression
190
Bibliography
192
Index
195
|
| adam_txt |
Contents
Preface
1
■J
page
ix
Insurance
data
1
1.1
Introduction
2
1.2
Types of variables
3
1.3
Data transformations
4
1.4
Data exploration
6
1.5
Grouping and runoff triangles
10
1.6
Assessing distributions
12
1.7
Data issues and biases
13
1.8
Data sets used
14
1.9
Outline of rest of book
19
Response distributions
20
2.1
Discrete and continuous random variables
20
2.2
Bernoulli
21
2.3
Binomial
22
2.4
Poisson
23
2.5
Negative binomial
24
2.6
Normal
26
2.7
Chi-square and gamma
27
2.8
Inverse Gaussian
29
2.9
Overdispersion
30
Exercises
33
Exponential family responses and estimation
35
3.1
Exponential family
35
3.2
The variance function
36
3.3
Proof of the mean and variance expressions
37
3.4
Standard distributions in the exponential family form
37
3.5
Fitting probability functions to data
39
Exercises
41
vi
Contents
4
Linear
modeling
42
4.1
History and terminology of linear modeling
42
4.2
What does "linear" in linear model mean?
43
4.3
Simple linear modeling
43
4.4
Multiple linear modeling
44
4.5
The classical linear model
46
4.6
Least squares properties under the classical linear model
47
4.7
Weighted least squares
47
4.8
Grouped and ungrouped data
48
4.9
Transformations to normality and linearity
49
4.10
Categorical explanatory variables
51
4.11
Polynomial regression
53
4.12
Banding continuous explanatory variables
54
4.13
Interaction
55
4.14
Collinearity
55
4.15
Hypothesis testing
56
4.16
Checks using the residuals
58
4.17
Checking explanatory variable specifications
60
4.18
Outliers
61
4.19
Model selection
62
5
Generalized linear models
64
5.1
The generalized linear model
64
5.2
Steps in generalized linear modeling
65
5.3
Links and canonical links
66
5.4
Offsets
66
5.5
Maximum likelihood estimation
67
5.6
Confidence intervals and prediction
70
5.7
Assessing fits and the deviance
71
5.8
Testing the significance of explanatory variables
74
5.9
Residuals
77
5.10
Further diagnostic tools
79
5.11
Model selection
80
Exercises
80
6
Models for count data
81
6.1
Poisson
regression
81
6.2
Poisson overdispersion
and negative binomial regression
89
6.3
Quasi-likelihood
94
6.4
Counts and frequencies
96
Exercises
96
7
Categorical responses
97
7.1
Binary responses
97
7.2
Logistic regression
98
Contents
vii
7.3 Application
of logistic regression to vehicle insurance
99
7.4
Correcting for exposure
102
7.5
Grouped binary data
105
7.6
Goodness of fit for logistic regression
107
7.7
Categorical responses with more than two categories
110
7.8
Ordinal responses 111
7.9
Nominal responses
116
Exercises
119
8
Continuous responses
120
8.1
Gamma regression
120
8.2
Inverse Gaussian regression
125
8.3
Tweedie regression
127
Exercises
128
9
Correlated data
129
9.1
Random effects
131
9.2
Specification of within-cluster correlation
136
9.3
Generalized estimating equations
137
Exercise
140
10
Extensions to the generalized linear model
141
10.1
Generalized additive models
141
10.2
Double generalized linear models
143
10.3
Generalized additive models for location, scale and shape
143
10.4
Zero-adjusted inverse Gaussian regression
145
10.5
A mean and dispersion model for total claim size
148
Exercises
149
Appendix
1
Computer code and output
150
ALI
Poisson
regression
150
Al.
2
Negative binomial regression
156
A
1.3
Quasi-likelihood regression
159
A
1.4
Logistic regression
160
Al.
5
Ordinal regression
169
Al.
6
Nominal regression
175
Al.
7
Gamma regression
178
A
1.8
Inverse Gaussian regression
181
A
1.9
Logistic regression GLMM
183
ALIO
Logistic regression GEE
185
ALII Logistic regression GAM
187
A1.12GAMLSS
189
Al.
13
Zero-adjusted inverse Gaussian regression
190
Bibliography
192
Index
195 |
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| id | DE-604.BV023340442 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:01:27Z |
| indexdate | 2024-07-09T21:16:21Z |
| institution | BVB |
| isbn | 9780521879149 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016524214 |
| oclc_num | 166382264 |
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| physical | x, 196 Seiten Illustrationen, Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | International series on actuarial science |
| spelling | De Jong, Piet (DE-588)170151522 aut Generalized linear models for insurance data Piet de Jong ; Department of Actuarial Studies, Macquarie University, Sydney ; Gillian Z. Heller ; Department of Statistics, Macquarie University, Sydney frist published Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo ; Delhi Cambridge University Press 2008 x, 196 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier International series on actuarial science Hier auch später erschienene, unveränderte Nachdrucke Mathematik Insurance / Mathematics Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 s Verallgemeinertes lineares Modell (DE-588)4124382-1 s DE-604 Heller, Gillian Z. (DE-588)1310631409 aut Erscheint auch als Online-Ausgabe 978-0-511-75540-8 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016524214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Jong, Piet Heller, Gillian Z. Generalized linear models for insurance data Mathematik Insurance / Mathematics Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4124382-1 (DE-588)4063194-1 |
| title | Generalized linear models for insurance data |
| title_auth | Generalized linear models for insurance data |
| title_exact_search | Generalized linear models for insurance data |
| title_exact_search_txtP | Generalized linear models for insurance data |
| title_full | Generalized linear models for insurance data Piet de Jong ; Department of Actuarial Studies, Macquarie University, Sydney ; Gillian Z. Heller ; Department of Statistics, Macquarie University, Sydney |
| title_fullStr | Generalized linear models for insurance data Piet de Jong ; Department of Actuarial Studies, Macquarie University, Sydney ; Gillian Z. Heller ; Department of Statistics, Macquarie University, Sydney |
| title_full_unstemmed | Generalized linear models for insurance data Piet de Jong ; Department of Actuarial Studies, Macquarie University, Sydney ; Gillian Z. Heller ; Department of Statistics, Macquarie University, Sydney |
| title_short | Generalized linear models for insurance data |
| title_sort | generalized linear models for insurance data |
| topic | Mathematik Insurance / Mathematics Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Mathematik Insurance / Mathematics Linear models (Statistics) Verallgemeinertes lineares Modell Versicherungsmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016524214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dejongpiet generalizedlinearmodelsforinsurancedata AT hellergillianz generalizedlinearmodelsforinsurancedata |