Statistics of extremes: theory and applications
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2005
|
| Edition: | Reprint. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 490 S. zahlr. graph. Darst. |
| ISBN: | 0471976474 9780471976479 |
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| 245 | 1 | 0 | |a Statistics of extremes |b theory and applications |c Jan Beirlant ... |
| 250 | |a Reprint. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2005 | |
| 300 | |a XIII, 490 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematical statistics | |
| 650 | 4 | |a Maxima and minima | |
| 650 | 0 | 7 | |a Extremwertstatistik |0 (DE-588)4153429-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Extremwertstatistik |0 (DE-588)4153429-3 |D s |
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| 856 | 4 | |u http://www.loc.gov/catdir/toc/wiley041/2004051046.html |3 Table of contents | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014168818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| adam_text | Contents
Preface
xi
1
WHY EXTREME VALUE THEORY?
1
1.1
A Simple Extreme Value Problem
.................. 1
1.2
Graphical Tools for Data Analysis
.................. 3
1.2.1
Quantile-quantile plots
.................... 3
1.2.2
Excess plots
......................... 14
1.3
Domains of Applications
....................... 19
1.3.1
Hydrology
.......................... 19
1.3.2
Environmental research and meteorology
.......... 21
1.3.3
Insurance applications
.................... 24
1.3.4
Finance applications
..................... 31
1.3.5
Geology and seismic analysis
................ 32
1.3.6
Metallurgy
.......................... 40
1.3.7
Miscellaneous applications
.................. 42
1.4
Conclusion
.............................. 42
2
THE PROBABILISTIC SIDE OF EXTREME
VALUE THEORY
45
2.1
The Possible Limits
.......................... 46
2.2
An Example
.............................. 51
2.3
The
Fréchet-Pareto
Case:
γ
> 0................... 56
2.3.1
The domain of attraction condition
............. 56
2.3.2
Condition on the underlying distribution
.......... 57
2.3.3
The historical approach
................... 58
2.3.4
Examples
........................... 58
2.3.5
Fitting data from a Pareto-type distribution
......... 61
2.4
The (Extremal) Weibull Case:
γ
< 0................ 65
2.4.1
The domain of attraction condition
............. 65
2.4.2
Condition on the underlying distribution
.......... 67
2.4.3
The historical approach
................... 67
2.4.4
Examples
........................... 67
vi
CONTENTS
2.5
The Gumbel Case:
γ
= 0 ...................... 69
2.5.1
The domain of attraction condition
............. 69
2.5.2
Condition on the underlying distribution
.......... 72
2.5.3
The historical approach and examples
............ 72
2.6
Alternative Conditions for (CY)
................... 73
2.7
Further on the Historical Approach
................. 75
2.8
Summary
............................... 76
2.9
Background Information
....................... 76
2.9.1
Inverse of a distribution
................... 77
2.9.2
Functions of regular variation
................ 77
2.9.3
Relation between
F
and
U
................. 79
2.9.4
Proofs for section
2.6.................... 80
3
AWAY FROM THE MAXIMUM
83
3.1
Introduction
.............................. 83
3.2
Order Statistics Close to the Maximum
............... 84
3.3
Second-order Theory
......................... 90
3.3.1
Remainder in terms of
U
.................. 90
3.3.2
Examples
........................... 92
3.3.3
Remainder in terms of
F
.................. 93
3.4
Mathematical Derivations
...................... 94
3.4.1
Proof of
(3.6)......................... 95
3.4.2
Proof of
(3.8)......................... 96
3.4.3
Solution of
(3.15) ...................... 97
3.4.4
Solution of
(3.18) ...................... 98
4
TAIL ESTIMATION UNDER PARETO-TYPE MODELS
99
4.1
A Naive Approach
.......................... 100
4.2
The Hill Estimator
.......................... 101
4.2.1
Construction
......................... 101
4.2.2
Properties
........................... 104
4.3
Other Regression Estimators
..................... 107
4.4
A Representation for Log-spacings and Asymptotic Results
.... 109
4.5
Reducing the Bias
.......................... 113
4.5.1
The quantile view
...................... 113
4.5.2
The probability view
..................... 117
4.6
Extreme Quantiles and Small Exceedance Probabilities
...... 119
4.6.1
First-order estimation of quantiles and return periods
... 119
4.6.2
Second-order refinements
.................. 121
4.7
Adaptive Selection of the Tail Sample Fraction
........... 123
5
TAIL ESTIMATION FOR ALL DOMAINS OF ATTRACTION
131
5.1
The Method of Block Maxima
.................... 132
5.1.1
The basic model
....................... 132
5.1.2
Parameter estimation
..................... 132
CONTENTS
vii
5.1.3
Estimation
of extreme quantiles
............... 135
5.1.4
Inference: confidence intervals
................ 137
5.2
Quantile View
—
Methods Based on (CY)
.............. 140
5.2.1
Pickands estimator
...................... 140
5.2.2
The moment estimator
.................... 142
5.2.3
Estimators based on the generalized quantile plot
..... 143
5.3
Tail Probability View—Peaks-Over-Threshold Method
....... 147
5.3.1
The basic model
....................... 147
5.3.2
Parameter estimation
..................... 149
5.4
Estimators Based on an Exponential Regression Model
...... 155
5.5
Extreme Tail Probability, Large Quantile and
Endpoint
Estimation
Using Threshold Methods
...................... 156
5.5.1
The quantile view
...................... 156
5.5.2
The probability view
..................... 158
5.5.3
Inference: confidence intervals
................ 159
5.6
Asymptotic Results Under
(CyHCţ)
................ 160
5.7
Reducing the Bias
.......................... 165
5.7.1
The quantile view
...................... 165
5.7.2
Extreme quantiles and small exceedance
probabilities
......................... 167
5.8
Adaptive Selection of the Tail Sample Fraction
........... 167
5.9
Appendices
.............................. 169
5.9.1
Information matrix for the GEV
............... 169
5.9.2
Point processes
........................ 169
5.9.3
GRV2 functions with
ρ
< 0................. 171
5.9.4
Asymptotic mean squared errors
.............. 172
5.9.5
AMSE
optimal ¿-values
................... 173
6
CASE STUDIES
177
6.1
The Condroz Data
.......................... 177
6.2
The
Secura
Belgian Re Data
..................... 188
6.2.1
The non-parametric approach
................ 189
6.2.2
Pareto-type modelling
.................... 191
6.2.3
Alternative extreme value methods
............. 195
6.2.4
Mixture modelling of claim sizes
.............. 198
6.3
Earthquake Data
........................... 200
7
REGRESSION ANALYSIS
209
7.1
Introduction
.............................. 210
7.2
The Method of Block Maxima
.................... 211
7.2.1
Model description
...................... 211
7.2.2
Maximum likelihood estimation
............... 212
7.2.3
Goodness-of-fit
........................ 213
7.2.4
Estimation of extreme conditional quantiles
........ 216
viii CONTENTS
7.3
The Quantile View
—
Methods Based on Exponential Regression
Models
................................ 218
7.3.1
Model description
...................... 218
7.3.2
Maximum likelihood estimation
............... 219
7.3.3
Goodness-of-fit
........................ 222
7.3.4
Estimation of extreme conditional quantiles
........ 223
7.4
The Tail Probability View—Peaks Over Threshold (POT)
Method
................................ 225
7.4.1
Model description
...................... 225
7.4.2
Maximum likelihood estimation
............... 226
7.4.3
Goodness-of-fit
........................ 229
7.4.4
Estimation of extreme conditional quantiles
........ 231
7.5
Non-parametric Estimation
...................... 233
7.5.1
Maximum penalized likelihood estimation
......... 234
7.5.2
Local polynomial maximum likelihood estimation
..... 238
7.6
Case Study
.............................. 241
8
MULTIVARIATE EXTREME VALUE THEORY
251
8.1
Introduction
.............................. 251
8.2
Multivariate Extreme Value Distributions
.............. 254
8.2.1
Max-stability and
max-infinite
divisibility
......... 254
8.2.2
Exponent measure
...................... 255
8.2.3
Spectral measure
....................... 258
8.2.4
Properties of max-stable distributions
............ 265
8.2.5
Bivariate case
......................... 267
8.2.6
Other choices for the margins
................ 271
8.2.7
Summary measures for extremal dependence
........ 273
8.3
The Domain of Attraction
...................... 275
8.3.1
General conditions
...................... 276
8.3.2
Convergence of the dependence structure
.......... 281
8.4
Additional Topics
........................... 287
8.5
Summary
............................... 290
8.6
Appendix
............................... 292
8.6.1
Computing spectral densities
................ 292
8.6.2
Representations of extreme value distributions
....... 293
9
STATISTICS OF MULTIVARIATE EXTREMES
297
9.1
Introduction
.............................. 297
9.2
Parametric Models
.......................... 300
9.2.1
Model construction methods
................. 300
9.2.2
Some parametric models
................... 304
9.3
Component-wise Maxima
...................... 313
9.3.1
Non-parametric estimation
.................. 314
9.3.2
Parametric estimation
.................... 318
9.3.3
Data example
......................... 321
CONTENTS ix
9.4
Excesses over a Threshold
...................... 325
9.4.1
Non-parametric estimation
.................. 326
9.4.2
Parametric estimation
.................... 333
9.4.3
Data example
......................... 338
9.5
Asymptotic Independence
...................... 342
9.5.1
Coefficients of extremal dependence
............ 343
9.5.2
Estimating the coefficient of tail dependence
........ 350
9.5.3
Joint tail modelling
...................... 354
9.6
Additional Topics
........................... 365
9.7
Summary
............................... 366
10
EXTREMES OF STATIONARY TIME SERIES
369
10.1
Introduction
.............................. 369
10.2
The Sample Maximum
........................ 371
10.2.1
The extremal limit theorem
................. 371
10.2.2
Data example
......................... 375
10.2.3
The extremal index
...................... 376
10.3
Point-Process Models
......................... 382
10.3.1
Clusters of extreme values
.................. 382
10.3.2
Cluster statistics
....................... 386
10.3.3
Excesses over threshold
................... 387
10.3.4
Statistical applications
.................... 389
10.3.5
Data example
......................... 395
10.3.6
Additional topics
....................... 399
10.4
Markov-Chain Models
........................ 401
10.4.1
The tail chain
......................... 401
10.4.2
Extremal index
........................ 405
10.4.3
Cluster statistics
....................... 406
10.4.4
Statistical applications
.................... 407
10.4.5
Fitting the Markov chain
................... 408
10.4.6
Additional topics
....................... 411
10.4.7
Data example
......................... 413
10.5
Multivariate Stationary Processes
.................. 419
10.5.1
The extremal limit theorem
................. 419
10.5.2
The multivariate extremal index
............... 421
10.5.3
Further reading
........................ 424
10.6
Additional Topics
........................... 425
11
BAYESIAN METHODOLOGY IN EXTREME VALUE
STATISTICS
429
11.1
Introduction
.............................. 429
11.2
The
Bayes
Approach
......................... 430
11.3
Prior Elicitation
............................ 431
11.4
Bayesian Computation
........................ 433
11.5
Univariate Inference
......................... 434
χ
CONTENTS
11.5.1
Inference based on block maxima
..............434
11.5.2
Inference for
Fréchet-Pareto-type
models
..........435
11.5.3
Inference for all domains of attractions
...........445
11.6
An Environmental Application
....................452
Bibliography
461
Author Index
479
Subject Index
485
|
| adam_txt |
Contents
Preface
xi
1
WHY EXTREME VALUE THEORY?
1
1.1
A Simple Extreme Value Problem
. 1
1.2
Graphical Tools for Data Analysis
. 3
1.2.1
Quantile-quantile plots
. 3
1.2.2
Excess plots
. 14
1.3
Domains of Applications
. 19
1.3.1
Hydrology
. 19
1.3.2
Environmental research and meteorology
. 21
1.3.3
Insurance applications
. 24
1.3.4
Finance applications
. 31
1.3.5
Geology and seismic analysis
. 32
1.3.6
Metallurgy
. 40
1.3.7
Miscellaneous applications
. 42
1.4
Conclusion
. 42
2
THE PROBABILISTIC SIDE OF EXTREME
VALUE THEORY
45
2.1
The Possible Limits
. 46
2.2
An Example
. 51
2.3
The
Fréchet-Pareto
Case:
γ
> 0. 56
2.3.1
The domain of attraction condition
. 56
2.3.2
Condition on the underlying distribution
. 57
2.3.3
The historical approach
. 58
2.3.4
Examples
. 58
2.3.5
Fitting data from a Pareto-type distribution
. 61
2.4
The (Extremal) Weibull Case:
γ
< 0. 65
2.4.1
The domain of attraction condition
. 65
2.4.2
Condition on the underlying distribution
. 67
2.4.3
The historical approach
. 67
2.4.4
Examples
. 67
vi
CONTENTS
2.5
The Gumbel Case:
γ
= 0 . 69
2.5.1
The domain of attraction condition
. 69
2.5.2
Condition on the underlying distribution
. 72
2.5.3
The historical approach and examples
. 72
2.6
Alternative Conditions for (CY)
. 73
2.7
Further on the Historical Approach
. 75
2.8
Summary
. 76
2.9
Background Information
. 76
2.9.1
Inverse of a distribution
. 77
2.9.2
Functions of regular variation
. 77
2.9.3
Relation between
F
and
U
. 79
2.9.4
Proofs for section
2.6. 80
3
AWAY FROM THE MAXIMUM
83
3.1
Introduction
. 83
3.2
Order Statistics Close to the Maximum
. 84
3.3
Second-order Theory
. 90
3.3.1
Remainder in terms of
U
. 90
3.3.2
Examples
. 92
3.3.3
Remainder in terms of
F
. 93
3.4
Mathematical Derivations
. 94
3.4.1
Proof of
(3.6). 95
3.4.2
Proof of
(3.8). 96
3.4.3
Solution of
(3.15) . 97
3.4.4
Solution of
(3.18) . 98
4
TAIL ESTIMATION UNDER PARETO-TYPE MODELS
99
4.1
A Naive Approach
. 100
4.2
The Hill Estimator
. 101
4.2.1
Construction
. 101
4.2.2
Properties
. 104
4.3
Other Regression Estimators
. 107
4.4
A Representation for Log-spacings and Asymptotic Results
. 109
4.5
Reducing the Bias
. 113
4.5.1
The quantile view
. 113
4.5.2
The probability view
. 117
4.6
Extreme Quantiles and Small Exceedance Probabilities
. 119
4.6.1
First-order estimation of quantiles and return periods
. 119
4.6.2
Second-order refinements
. 121
4.7
Adaptive Selection of the Tail Sample Fraction
. 123
5
TAIL ESTIMATION FOR ALL DOMAINS OF ATTRACTION
131
5.1
The Method of Block Maxima
. 132
5.1.1
The basic model
. 132
5.1.2
Parameter estimation
. 132
CONTENTS
vii
5.1.3
Estimation
of extreme quantiles
. 135
5.1.4
Inference: confidence intervals
. 137
5.2
Quantile View
—
Methods Based on (CY)
. 140
5.2.1
Pickands estimator
. 140
5.2.2
The moment estimator
. 142
5.2.3
Estimators based on the generalized quantile plot
. 143
5.3
Tail Probability View—Peaks-Over-Threshold Method
. 147
5.3.1
The basic model
. 147
5.3.2
Parameter estimation
. 149
5.4
Estimators Based on an Exponential Regression Model
. 155
5.5
Extreme Tail Probability, Large Quantile and
Endpoint
Estimation
Using Threshold Methods
. 156
5.5.1
The quantile view
. 156
5.5.2
The probability view
. 158
5.5.3
Inference: confidence intervals
. 159
5.6
Asymptotic Results Under
(CyHCţ)
. 160
5.7
Reducing the Bias
. 165
5.7.1
The quantile view
. 165
5.7.2
Extreme quantiles and small exceedance
probabilities
. 167
5.8
Adaptive Selection of the Tail Sample Fraction
. 167
5.9
Appendices
. 169
5.9.1
Information matrix for the GEV
. 169
5.9.2
Point processes
. 169
5.9.3
GRV2 functions with
ρ
< 0. 171
5.9.4
Asymptotic mean squared errors
. 172
5.9.5
AMSE
optimal ¿-values
. 173
6
CASE STUDIES
177
6.1
The Condroz Data
. 177
6.2
The
Secura
Belgian Re Data
. 188
6.2.1
The non-parametric approach
. 189
6.2.2
Pareto-type modelling
. 191
6.2.3
Alternative extreme value methods
. 195
6.2.4
Mixture modelling of claim sizes
. 198
6.3
Earthquake Data
. 200
7
REGRESSION ANALYSIS
209
7.1
Introduction
. 210
7.2
The Method of Block Maxima
. 211
7.2.1
Model description
. 211
7.2.2
Maximum likelihood estimation
. 212
7.2.3
Goodness-of-fit
. 213
7.2.4
Estimation of extreme conditional quantiles
. 216
viii CONTENTS
7.3
The Quantile View
—
Methods Based on Exponential Regression
Models
. 218
7.3.1
Model description
. 218
7.3.2
Maximum likelihood estimation
. 219
7.3.3
Goodness-of-fit
. 222
7.3.4
Estimation of extreme conditional quantiles
. 223
7.4
The Tail Probability View—Peaks Over Threshold (POT)
Method
. 225
7.4.1
Model description
. 225
7.4.2
Maximum likelihood estimation
. 226
7.4.3
Goodness-of-fit
. 229
7.4.4
Estimation of extreme conditional quantiles
. 231
7.5
Non-parametric Estimation
. 233
7.5.1
Maximum penalized likelihood estimation
. 234
7.5.2
Local polynomial maximum likelihood estimation
. 238
7.6
Case Study
. 241
8
MULTIVARIATE EXTREME VALUE THEORY
251
8.1
Introduction
. 251
8.2
Multivariate Extreme Value Distributions
. 254
8.2.1
Max-stability and
max-infinite
divisibility
. 254
8.2.2
Exponent measure
. 255
8.2.3
Spectral measure
. 258
8.2.4
Properties of max-stable distributions
. 265
8.2.5
Bivariate case
. 267
8.2.6
Other choices for the margins
. 271
8.2.7
Summary measures for extremal dependence
. 273
8.3
The Domain of Attraction
. 275
8.3.1
General conditions
. 276
8.3.2
Convergence of the dependence structure
. 281
8.4
Additional Topics
. 287
8.5
Summary
. 290
8.6
Appendix
. 292
8.6.1
Computing spectral densities
. 292
8.6.2
Representations of extreme value distributions
. 293
9
STATISTICS OF MULTIVARIATE EXTREMES
297
9.1
Introduction
. 297
9.2
Parametric Models
. 300
9.2.1
Model construction methods
. 300
9.2.2
Some parametric models
. 304
9.3
Component-wise Maxima
. 313
9.3.1
Non-parametric estimation
. 314
9.3.2
Parametric estimation
. 318
9.3.3
Data example
. 321
CONTENTS ix
9.4
Excesses over a Threshold
. 325
9.4.1
Non-parametric estimation
. 326
9.4.2
Parametric estimation
. 333
9.4.3
Data example
. 338
9.5
Asymptotic Independence
. 342
9.5.1
Coefficients of extremal dependence
. 343
9.5.2
Estimating the coefficient of tail dependence
. 350
9.5.3
Joint tail modelling
. 354
9.6
Additional Topics
. 365
9.7
Summary
. 366
10
EXTREMES OF STATIONARY TIME SERIES
369
10.1
Introduction
. 369
10.2
The Sample Maximum
. 371
10.2.1
The extremal limit theorem
. 371
10.2.2
Data example
. 375
10.2.3
The extremal index
. 376
10.3
Point-Process Models
. 382
10.3.1
Clusters of extreme values
. 382
10.3.2
Cluster statistics
. 386
10.3.3
Excesses over threshold
. 387
10.3.4
Statistical applications
. 389
10.3.5
Data example
. 395
10.3.6
Additional topics
. 399
10.4
Markov-Chain Models
. 401
10.4.1
The tail chain
. 401
10.4.2
Extremal index
. 405
10.4.3
Cluster statistics
. 406
10.4.4
Statistical applications
. 407
10.4.5
Fitting the Markov chain
. 408
10.4.6
Additional topics
. 411
10.4.7
Data example
. 413
10.5
Multivariate Stationary Processes
. 419
10.5.1
The extremal limit theorem
. 419
10.5.2
The multivariate extremal index
. 421
10.5.3
Further reading
. 424
10.6
Additional Topics
. 425
11
BAYESIAN METHODOLOGY IN EXTREME VALUE
STATISTICS
429
11.1
Introduction
. 429
11.2
The
Bayes
Approach
. 430
11.3
Prior Elicitation
. 431
11.4
Bayesian Computation
. 433
11.5
Univariate Inference
. 434
χ
CONTENTS
11.5.1
Inference based on block maxima
.434
11.5.2
Inference for
Fréchet-Pareto-type
models
.435
11.5.3
Inference for all domains of attractions
.445
11.6
An Environmental Application
.452
Bibliography
461
Author Index
479
Subject Index
485 |
| any_adam_object | 1 |
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| edition | Reprint. |
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| id | DE-604.BV020847053 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:18:35Z |
| indexdate | 2024-07-09T20:26:31Z |
| institution | BVB |
| isbn | 0471976474 9780471976479 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014168818 |
| oclc_num | 254602467 |
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| physical | XIII, 490 S. zahlr. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Statistics of extremes theory and applications Jan Beirlant ... Reprint. Chichester [u.a.] Wiley 2005 XIII, 490 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index Mathematical statistics Maxima and minima Extremwertstatistik (DE-588)4153429-3 gnd rswk-swf Extremwertstatistik (DE-588)4153429-3 s DE-604 Beirlant, Jan Sonstige (DE-588)170449963 oth http://www.loc.gov/catdir/description/wiley042/2004051046.html Publisher description http://www.loc.gov/catdir/toc/wiley041/2004051046.html Table of contents Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014168818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Statistics of extremes theory and applications Mathematical statistics Maxima and minima Extremwertstatistik (DE-588)4153429-3 gnd |
| subject_GND | (DE-588)4153429-3 |
| title | Statistics of extremes theory and applications |
| title_auth | Statistics of extremes theory and applications |
| title_exact_search | Statistics of extremes theory and applications |
| title_exact_search_txtP | Statistics of extremes theory and applications |
| title_full | Statistics of extremes theory and applications Jan Beirlant ... |
| title_fullStr | Statistics of extremes theory and applications Jan Beirlant ... |
| title_full_unstemmed | Statistics of extremes theory and applications Jan Beirlant ... |
| title_short | Statistics of extremes |
| title_sort | statistics of extremes theory and applications |
| title_sub | theory and applications |
| topic | Mathematical statistics Maxima and minima Extremwertstatistik (DE-588)4153429-3 gnd |
| topic_facet | Mathematical statistics Maxima and minima Extremwertstatistik |
| url | http://www.loc.gov/catdir/description/wiley042/2004051046.html http://www.loc.gov/catdir/toc/wiley041/2004051046.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014168818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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