An introduction to copulas:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer
2006
|
| Edition: | 2. ed. |
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | BTU01 GEM01 TUM01 UBA01 UBM01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9780387286594 9780387286785 |
| DOI: | 10.1007/0-387-28678-0 |
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Record in the Search Index
| _version_ | 1804136659859537920 |
|---|---|
| adam_text | Contents
Preface to the First Edition _vü
Preface to the Second Edition ix
1 Introduction 1
2 Definitions and Basic Properties 7
2.1 Preliminaries 7
2.2 Copulas 10
Exercises 2.1 2.11 14
2.3 Sklar s Theorem 17
2.4 Copulas and Random Variables 24
Exercises 2.12 2.17 28
2.5 The Frechet Hoeffding Bounds for Joint Distribution
Functions of Random Variables 30
2.6 Survival Copulas 32
Exercises 2.18 2.26 34
2.7 Symmetry 36
2.8 Order 38
Exercises 2.27 2.33 39
2.9 Random Variate Generation .40
2.10 Multivariate Copulas .42
Exercises 2.34 2.37 .48
3 Methods of Constructing Copulas 51
3.1 The Inversion Method 51
3.1.1 The Marshall Olkin Bivariate Exponential Distribution 52
3.1.2 The Circular Uniform Distribution 55
Exercises 3.1 3.6 57
3.2 Geometrie Methods 59
3.2.1 Singular Copulas with Prescribed Support 59
3.2.2 Ordinal Sums 63
Exercises 3.7 3.13 64
3.2.3 Shuffles of M 67
3.2.4 Convex Sums 72
Exercises 3.14 3.20 .74
3.2.5 Copulas with Prescribed Horizontal or Vertical Sections....76
3.2.6 Copulas with Prescribed Diagonal Sections 84
xii Contents
Exercises 3.21 3.34 86
3.3 Algebraic Methods 89
3.3.1 Plackett Distributions 89
3.3.2 Ali Mikhail Haq Distributions 92
3.3.3 A Copula Transformation Method 94
3.3.4 Extreme Value Copulas 97
Exercises 3.35 3.42 99
3.4 Copulas with Specified Properties ¦ 101
3.4.1 Harmonie Copulas 101
3.4.2 Homogeneous Copulas 101
3.4.3 Concave and Convex Copulas 102
3.5 Constructing Multivariate Copulas 105
4 Archimedean Copulas 109
4.1 Definitions 109
4.2 One parameter Families 114
4.3 Fundamental Properties 115
Exercises 4.1 4.17 132
4.4 Order and Limiting Cases 135
4.5 Two parameter Families 141
4.5.1 Families of Generators 141
4.5.2 Rational Archimedean Copulas 146
Exercises 4.18 4.23 150
4.6 Multivariate Archimedean Copulas 151
Exercises 4.24 4.25 155
5 Dependence 157
5.1 Concordance 157
5.1.1 Kendall s tau 158
Exercises 5.1 5.5 165
5.1.2 Spearman s rho 167
Exercises 5.6 5.15 171
5.1.3 The Relationship between Kendall s tau
and Spearman s rho 174
5.1.4 Other Concordance Measures 180
Exercises 5.16 5.21 185
5.2 Dependence Properties. 186
5.2.1 Quadrant Dependence 187
Exercises 5.22 5.29 189
5.2.2 Tail Monotonicity 191
5.2.3 Stochastic Monotonicity, Corner Set Monotonicity,
and Likelihood Ratio Dependence 195
Exercises 5.30 5.39 .204
5.3 Other Measures of Association. 207
5.3.1 Measures of Dependence .207
5.3.2 Measures Based on Gini s Coefficient ..211
Exercises 5.40 5.46. .213
5.4 Tail Dependence .214
1
Contents xiii
Exercises 5.47 5.50 216
5.5 Mediän Regression. 217
5.6 Empirical Copulas 219
5.7 Multivariate Dependence 222
6 Additional Topics 227
6.1 Distributions with Fixed Margins 227
Exercises 6.1 6.5 233
6.2 Quasi copulas 236
Exercises 6.6 6.8 240
6.3 Operations on Distribution Functions 241
6.4 Markov Processes 244
Exercises 6.9 6.13 248
References 251
List of Symbols 263
Index 265
|
| adam_txt |
Contents
Preface to the First Edition _vü
Preface to the Second Edition ix
1 Introduction 1
2 Definitions and Basic Properties 7
2.1 Preliminaries 7
2.2 Copulas 10
Exercises 2.1 2.11 14
2.3 Sklar's Theorem 17
2.4 Copulas and Random Variables 24
Exercises 2.12 2.17 28
2.5 The Frechet Hoeffding Bounds for Joint Distribution
Functions of Random Variables 30
2.6 Survival Copulas 32
Exercises 2.18 2.26 34
2.7 Symmetry 36
2.8 Order 38
Exercises 2.27 2.33 39
2.9 Random Variate Generation .40
2.10 Multivariate Copulas .42
Exercises 2.34 2.37 .48
3 Methods of Constructing Copulas 51
3.1 The Inversion Method 51
3.1.1 The Marshall Olkin Bivariate Exponential Distribution 52
3.1.2 The Circular Uniform Distribution 55
Exercises 3.1 3.6 57
3.2 Geometrie Methods 59
3.2.1 Singular Copulas with Prescribed Support 59
3.2.2 Ordinal Sums 63
Exercises 3.7 3.13 64
3.2.3 Shuffles of M 67
3.2.4 Convex Sums 72
Exercises 3.14 3.20 .74
3.2.5 Copulas with Prescribed Horizontal or Vertical Sections.76
3.2.6 Copulas with Prescribed Diagonal Sections 84
xii Contents
Exercises 3.21 3.34 86
3.3 Algebraic Methods 89
3.3.1 Plackett Distributions 89
3.3.2 Ali Mikhail Haq Distributions 92
3.3.3 A Copula Transformation Method 94
3.3.4 Extreme Value Copulas 97
Exercises 3.35 3.42 99
3.4 Copulas with Specified Properties ¦ 101
3.4.1 Harmonie Copulas 101
3.4.2 Homogeneous Copulas 101
3.4.3 Concave and Convex Copulas 102
3.5 Constructing Multivariate Copulas 105
4 Archimedean Copulas 109
4.1 Definitions 109
4.2 One parameter Families 114
4.3 Fundamental Properties 115
Exercises 4.1 4.17 132
4.4 Order and Limiting Cases 135
4.5 Two parameter Families 141
4.5.1 Families of Generators 141
4.5.2 Rational Archimedean Copulas 146
Exercises 4.18 4.23 150
4.6 Multivariate Archimedean Copulas 151
Exercises 4.24 4.25 155
5 Dependence 157
5.1 Concordance 157
5.1.1 Kendall's tau 158
Exercises 5.1 5.5 165
5.1.2 Spearman's rho 167
Exercises 5.6 5.15 171
5.1.3 The Relationship between Kendall's tau
and Spearman's rho 174
5.1.4 Other Concordance Measures 180
Exercises 5.16 5.21 185
5.2 Dependence Properties. 186
5.2.1 Quadrant Dependence 187
Exercises 5.22 5.29 189
5.2.2 Tail Monotonicity 191
5.2.3 Stochastic Monotonicity, Corner Set Monotonicity,
and Likelihood Ratio Dependence 195
Exercises 5.30 5.39 .204
5.3 Other Measures of Association. 207
5.3.1 Measures of Dependence .207
5.3.2 Measures Based on Gini's Coefficient .211
Exercises 5.40 5.46. .213
5.4 Tail Dependence .214
1
Contents xiii
Exercises 5.47 5.50 216
5.5 Mediän Regression. 217
5.6 Empirical Copulas 219
5.7 Multivariate Dependence 222
6 Additional Topics 227
6.1 Distributions with Fixed Margins 227
Exercises 6.1 6.5 233
6.2 Quasi copulas 236
Exercises 6.6 6.8 240
6.3 Operations on Distribution Functions 241
6.4 Markov Processes 244
Exercises 6.9 6.13 248
References 251
List of Symbols 263
Index 265 |
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| author | Nelsen, Roger B. 1942- |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/0-387-28678-0 |
| edition | 2. ed. |
| format | Electronic eBook |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Einführung Aufgabensammlung |
| id | DE-604.BV022544782 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:11:30Z |
| indexdate | 2024-07-09T20:59:55Z |
| institution | BVB |
| isbn | 9780387286594 9780387286785 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015751176 |
| oclc_num | 315555722 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-634 DE-M382 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-634 DE-M382 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 DE-19 DE-BY-UBM |
| physical | 1 Online-Ressource |
| psigel | ZDB-2-SMA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Nelsen, Roger B. 1942- Verfasser (DE-588)12076945X aut An introduction to copulas Roger B. Nelsen 2. ed. New York, NY Springer 2006 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Springer series in statistics Multivariate Normalverteilung (DE-588)4227589-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Kopula Mathematik (DE-588)4529954-7 gnd rswk-swf Verteilungsfunktion (DE-588)4192219-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content Kopula Mathematik (DE-588)4529954-7 s DE-604 Verteilungsfunktion (DE-588)4192219-0 s 3\p DE-604 Multivariate Normalverteilung (DE-588)4227589-1 s 4\p DE-604 Multivariate Analyse (DE-588)4040708-1 s 5\p DE-604 https://doi.org/10.1007/0-387-28678-0 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015751176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nelsen, Roger B. 1942- An introduction to copulas Multivariate Normalverteilung (DE-588)4227589-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd Kopula Mathematik (DE-588)4529954-7 gnd Verteilungsfunktion (DE-588)4192219-0 gnd |
| subject_GND | (DE-588)4227589-1 (DE-588)4040708-1 (DE-588)4529954-7 (DE-588)4192219-0 (DE-588)4151278-9 (DE-588)4143389-0 |
| title | An introduction to copulas |
| title_auth | An introduction to copulas |
| title_exact_search | An introduction to copulas |
| title_exact_search_txtP | An introduction to copulas |
| title_full | An introduction to copulas Roger B. Nelsen |
| title_fullStr | An introduction to copulas Roger B. Nelsen |
| title_full_unstemmed | An introduction to copulas Roger B. Nelsen |
| title_short | An introduction to copulas |
| title_sort | an introduction to copulas |
| topic | Multivariate Normalverteilung (DE-588)4227589-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd Kopula Mathematik (DE-588)4529954-7 gnd Verteilungsfunktion (DE-588)4192219-0 gnd |
| topic_facet | Multivariate Normalverteilung Multivariate Analyse Kopula Mathematik Verteilungsfunktion Einführung Aufgabensammlung |
| url | https://doi.org/10.1007/0-387-28678-0 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015751176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nelsenrogerb anintroductiontocopulas |