Introductory statistics with applications in general insurance:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Pr.
1999
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 281 S. graph. Darst. |
| ISBN: | 052165534X 0521652340 |
Internformat
MARC
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| 100 | 1 | |a Hossack, I. B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory statistics with applications in general insurance |c I. B. Hossack ; J. H. Pollard ; B. Zehnwirth |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1999 | |
| 300 | |a 281 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Assurance - Méthodes statistiques | |
| 650 | 7 | |a Estatística |2 larpcal | |
| 650 | 4 | |a Insurance - Statistical methods | |
| 650 | 7 | |a Seguro (métodos estatísticos) |2 larpcal | |
| 650 | 4 | |a Statistiques | |
| 650 | 7 | |a Statistische methoden |2 gtt | |
| 650 | 7 | |a Verzekeringswezen |2 gtt | |
| 650 | 7 | |a Verzekeringswiskunde |2 gtt | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Insurance |x Statistical methods | |
| 650 | 4 | |a Statistics | |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Versicherung |0 (DE-588)4063173-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Statistik |0 (DE-588)4056995-0 |D s |
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| 700 | 1 | |a Pollard, John Hurlstone |e Verfasser |4 aut | |
| 700 | 1 | |a Zehnwirth, Benjamin |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008526851 | ||
Datensatz im Suchindex
| _version_ | 1804127204783685632 |
|---|---|
| adam_text | CONTENTS
Preface to first edition jx
Preface to second edition xi
1 Introduction and mathematical preliminaries 1
1.1 Introduction 1
1.2 Summation notation 2
1.3 Factorial notation n 2
1.4 Combinatorial notation/ ) 3
1.5 Power notation 5
1.6 Differentiation; the slope of a curve 6
1.7 Maxima and minima 10
* 1.8 Functions of more than one variable; maxima and minima 12
1.9 The exponential function ex 14
1.10 The natural logarithm function In x 18
1.11 Exercises 23
2 Elementary probability 25
2.1 Introduction; concept of probability 25
2.2 Joint and disjoint events; intersection and union 26
2.3 Conditional probability 30
2.4 Independence of two events 31
2.5 Exercises 32
3 Random variables and their distributions 34
3.1 Discrete random variables and their distributions 34
3.2 Continuous random variables and their distributions 38
3.3 The area under a curve; integration and differentiation 42
3.4 Exercises 50
4 Location and dispersion 52
4.1 Measures of location mean, median and mode 52
4.2 Dispersion variance and standard deviation 57
**4.3 Expectations and moments 61
**4.4 Conditional means 63
**4.5 Conditional variances 64
**4.6 Skewness 65
4.7 Exercises 66
5 Statistical distributions useful in general insurance work 68
5.1 The normal distribution 68
5.2 The Central Limit Theorem 77
Contents vi
5.3 The log normal distribution 81
*5.4 The Pareto distribution 84
*5.5 The gamma distribution 86
5.6 The Poisson distribution 87
5.7 Normal approximation to the Poisson distribution 91
*5.8 The binomial distribution 93
* *5.9 The negative binomial distribution; heterogeneity of risk 96
5.10 The importance of theoretical distributions in general insurance 101
5.11 Exercises 102
6 Inferences fiom general insurance data 103
6.1 Hypothesis testing 103
6.2 Point estimation and method of moments 107
*6.3 Maximum likelihood 108
*6.4 Confidence intervals 110
*6.5 Risk factors; multivariate models; least squares 112
6.6 Exercises 120
7 The risk premium 122
7.1 Risk premium; claim frequency and claim size 122
7.2 Claim frequency rate; exposure 123
7.3 Claim size; pitfalls 128
7.4 Claim settlement pattern 137
*7.5 Excesses and excess of loss reinsurances 145
7.6 Exercises 150
8 Experience rating 151
8.1 Introduction 151
8.2 Credibility theory 156
8.3 Full credibility 157
8.4 Partial credibility 160
*8.5 Bayes Theorem 161
**8.6 A Bayesian approach to the updating of claim frequency rates 162
8.7 No claim discount (NCD) 166
8.8 Exercises 175
9 Simulation 177
9.1 Random numbers and simulation 177
9.2 How many simulations? 182
9.3 Computer generation of random numbers 184
9.4 Linear congruential generators 184
9.5 Random observations on the normal distribution 186
9.6 Random observations on the log normal distribution 188
9.7 Random observations on the Poisson distribution 189
*9.8 Random observations on the negative binomial distribution 192
9.9 A simulation example 193
9.10 When to simulate 195
9.11 Simulation of an NCD system 198
9.12 Limitations of the model; sensitivity analysis 203
9.13 Exercises 204
Contents vn
10 Estimation of outstanding claim provisions 206
10.1 Delays in claim reporting and claim settlement; run off 206
10.2 The run off triangle 207
10.3 Chain ladder method without inflation adjustment 208
10.4 Does the chain ladder model fit the data? 211
10.5 Chain ladder method with inflation adjustment 213
10.6 The separation method (direct future payments approach) 223
*10.7 The separation method (two other approaches) 231
10.8 IBNR, and the chain ladder and separation methods 233
10.9 Alternative methods of assessing outstanding claim provisions 234
10.10 The tail 234
10.11 Estimation of IBNR claim provisions 237
10.12 Exercises 241
11 Elementary risk theory 243
11.1 Introduction 243
11.2 Portfolio with constant (fixed) claim size 245
11.3 Variable claim size 248
**11.4 The expectation and variance of C 255
11.5 The assumption of normality 255
11.6 Summary and further reading 257
11.7 Exercises 259
References 260
Solutions to exercises 262
Author index 275
Subject index 277
|
| any_adam_object | 1 |
| author | Hossack, I. B. Pollard, John Hurlstone Zehnwirth, Benjamin |
| author_facet | Hossack, I. B. Pollard, John Hurlstone Zehnwirth, Benjamin |
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| building | Verbundindex |
| bvnumber | BV012558211 |
| callnumber-first | H - Social Science |
| callnumber-label | HG8781 |
| callnumber-raw | HG8781 |
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| callnumber-subject | HG - Finance |
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| ctrlnum | (OCoLC)40609880 (DE-599)BVBBV012558211 |
| dewey-full | 519.5/024/368 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/024/368 |
| dewey-search | 519.5/024/368 |
| dewey-sort | 3519.5 224 3368 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV012558211 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:29:38Z |
| institution | BVB |
| isbn | 052165534X 0521652340 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008526851 |
| oclc_num | 40609880 |
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| owner_facet | DE-739 DE-355 DE-BY-UBR DE-M347 DE-634 |
| physical | 281 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| spelling | Hossack, I. B. Verfasser aut Introductory statistics with applications in general insurance I. B. Hossack ; J. H. Pollard ; B. Zehnwirth 2. ed. Cambridge u.a. Cambridge Univ. Pr. 1999 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Assurance - Méthodes statistiques Estatística larpcal Insurance - Statistical methods Seguro (métodos estatísticos) larpcal Statistiques Statistische methoden gtt Verzekeringswezen gtt Verzekeringswiskunde gtt Statistik Insurance Statistical methods Statistics Statistik (DE-588)4056995-0 gnd rswk-swf Versicherung (DE-588)4063173-4 gnd rswk-swf Versicherung (DE-588)4063173-4 s Statistik (DE-588)4056995-0 s DE-604 Pollard, John Hurlstone Verfasser aut Zehnwirth, Benjamin Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008526851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hossack, I. B. Pollard, John Hurlstone Zehnwirth, Benjamin Introductory statistics with applications in general insurance Assurance - Méthodes statistiques Estatística larpcal Insurance - Statistical methods Seguro (métodos estatísticos) larpcal Statistiques Statistische methoden gtt Verzekeringswezen gtt Verzekeringswiskunde gtt Statistik Insurance Statistical methods Statistics Statistik (DE-588)4056995-0 gnd Versicherung (DE-588)4063173-4 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4063173-4 |
| title | Introductory statistics with applications in general insurance |
| title_auth | Introductory statistics with applications in general insurance |
| title_exact_search | Introductory statistics with applications in general insurance |
| title_full | Introductory statistics with applications in general insurance I. B. Hossack ; J. H. Pollard ; B. Zehnwirth |
| title_fullStr | Introductory statistics with applications in general insurance I. B. Hossack ; J. H. Pollard ; B. Zehnwirth |
| title_full_unstemmed | Introductory statistics with applications in general insurance I. B. Hossack ; J. H. Pollard ; B. Zehnwirth |
| title_short | Introductory statistics with applications in general insurance |
| title_sort | introductory statistics with applications in general insurance |
| topic | Assurance - Méthodes statistiques Estatística larpcal Insurance - Statistical methods Seguro (métodos estatísticos) larpcal Statistiques Statistische methoden gtt Verzekeringswezen gtt Verzekeringswiskunde gtt Statistik Insurance Statistical methods Statistics Statistik (DE-588)4056995-0 gnd Versicherung (DE-588)4063173-4 gnd |
| topic_facet | Assurance - Méthodes statistiques Estatística Insurance - Statistical methods Seguro (métodos estatísticos) Statistiques Statistische methoden Verzekeringswezen Verzekeringswiskunde Statistik Insurance Statistical methods Statistics Versicherung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008526851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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