Loss data analysis: the maximum entropy approach
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2023]
|
| Edition: | 2nd, extended edition |
| Series: | De Gruyter STEM
|
| Subjects: | |
| Online Access: | https://www.degruyter.com/isbn/9783111047386 Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XII, 210 Seiten Diagramme 24 cm x 17 cm, 384 g |
| ISBN: | 9783111047386 3111047385 |
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MARC
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| 016 | 7 | |a 1274463556 |2 DE-101 | |
| 020 | |a 9783111047386 |c Broschur: EUR 69.95 (DE) (freier Preis), EUR 69.95 (AT) (freier Preis) |9 978-3-11-104738-6 | ||
| 020 | |a 3111047385 |9 3-11-104738-5 | ||
| 024 | 3 | |a 9783111047386 | |
| 035 | |a (OCoLC)1376411576 | ||
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| 100 | 1 | |a Gzyl, Henryk |d 1946- |e Verfasser |0 (DE-588)172111188 |4 aut | |
| 245 | 1 | 0 | |a Loss data analysis |b the maximum entropy approach |c Henryk Gzyl, Silvia Mayoral, and Erika Gomes-Gonçalves |
| 250 | |a 2nd, extended edition | ||
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2023] | |
| 300 | |a XII, 210 Seiten |b Diagramme |c 24 cm x 17 cm, 384 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter STEM | |
| 650 | 0 | 7 | |a Risikoanalyse |0 (DE-588)4137042-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maximum-Entropie-Methode |0 (DE-588)4277537-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |2 gnd |9 rswk-swf |
| 653 | |a Loss probability determination | ||
| 653 | |a risk aggregation | ||
| 653 | |a risk disaggregation | ||
| 653 | |a maximum entropy method | ||
| 653 | |a Maxentropic Laplace transform inversion. | ||
| 653 | |a Loss probability determination; risk aggregation; risk disaggregation; maximum entropy method; Maxentropic Laplace transform inversion. | ||
| 653 | |a Risikoanalyse | ||
| 653 | |a Datenanalyse | ||
| 653 | |a TB: Textbook | ||
| 689 | 0 | 0 | |a Risikoanalyse |0 (DE-588)4137042-9 |D s |
| 689 | 0 | 1 | |a Maximum-Entropie-Methode |0 (DE-588)4277537-1 |D s |
| 689 | 0 | 2 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Mayoral, Silvia |e Verfasser |0 (DE-588)1160062056 |4 aut | |
| 700 | 1 | |a Gomes-Gonçalves, Erika |e Verfasser |0 (DE-588)116006251X |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-104970-0 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-104818-5 |
| 856 | 4 | 2 | |m X:MVB |u https://www.degruyter.com/isbn/9783111047386 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1274463556/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034136814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a vlb |d 20221202 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
Record in the Search Index
| _version_ | 1805066153068855296 |
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| adam_text |
CONTENTS
PREFACE
-
VII
1
1.1
1.2
INTRODUCTION
-
1
THE
BASIC
LOSS
AGGREGATION
PROBLEM
-
1
DESCRIPTION
OF
THE
CONTENTS
-
2
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.2
2.3
2.3.1
2.3.2
FREQUENCY
MODELS
-
5
A
SHORT
LIST
OF
EXAMPLES
-
5
THE
POISSON
DISTRIBUTION
-
6
POISSON
MIXTURES
-
7
THE
NEGATIVE
BINOMIAL
DISTRIBUTION
-
8
BINOMIAL
MODELS
-
9
UNIFIED
VERSION
-
9
EXAMPLES
-
10
DETERMINING
THE
PARAMETER
OF
A
POISSON
DISTRIBUTION
-
11
BINOMIAL
DISTRIBUTION
-
18
3
3.1
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.1.6
3.2
3.2.1
INDIVIDUAL
SEVERITY
MODELS
-
22
A
SHORT
CATALOG
OF
DISTRIBUTIONS
-
22
EXPONENTIAL
DISTRIBUTION
-
22
THE
SIMPLE
PARETO
DISTRIBUTION
-
23
GAMMA
DISTRIBUTION
-
23
THE
LOGNORMAL
DISTRIBUTION
-
24
THE
BETA
DISTRIBUTION
-
24
A
MIXTURE
OF
DISTRIBUTIONS
-
25
NUMERICAL
EXAMPLES
-
25
DATA
FROM
A
DENSITY
-
26
4
4.1
4.2
4.3
4.4
4.5
SOME
DETAILED
EXAMPLES
-
30
CLAIM
DISTRIBUTION
AND
OPERATIONAL
RISK
LOSSES
-
30
SIMPLE
MODEL
OF
CREDIT
RISK
-
31
SHOCK
AND
DAMAGE
MODELS
-
35
BARRIER
CROSSING
TIMES
-
35
APPLICATIONS
IN
RELIABILITY
THEORY
-
36
5
5.1
5.1.1
5.2
5.2.1
SOME
TRADITIONAL
APPROACHES
TO
THE
AGGREGATION
PROBLEM
-
38
GENERAL
REMARKS
-
38
GENERAL
ISSUES
-
39
ANALYTICAL
TECHNIQUES:
THE
MOMENT
GENERATING
FUNCTION
-
40
SIMPLE
EXAMPLES
-
41
X
-
-
CONTENTS
5.3
5.3.1
5.3.2
5.3.3
5.4
5.4.1
5.4.2
5.4.3
5.5
5.6
APPROXIMATE
METHODS
-
44
THE
CASE
OF
COMPUTABLE
CONVOLUTIONS
-
44
SIMPLE
APPROXIMATIONS
TO
THE
TOTAL
LOSS
DISTRIBUTION
-
45
EDGEWORTH
APPROXIMATION
-
46
NUMERICAL
TECHNIQUES
-
48
CALCULATIONS
STARTING
FROM
EMPIRICAL
OR
SIMULATED
DATA
-
48
RECURRENCE
RELATIONS
-
49
FURTHER
NUMERICAL
ISSUES
-
50
NUMERICAL
EXAMPLES
-
50
CONCLUDING
REMARKS
-
60
6
6.1
6.2
6.3
6.4
6.5
6.5.1
6.5.2
6.6
6.6.1
6.6.2
LAPLACE
TRANSFORMS
AND
FRACTIONAL
MOMENT
PROBLEMS
-
62
MATHEMATICAL
PROPERTIES
OF
THE
LAPLACE
TRANSFORM
AND
ITS
INVERSE
-
62
INVERSION
OF
THE
LAPLACE
TRANSFORM
-
64
LAPLACE
TRANSFORM
AND
FRACTIONAL
MOMENTS
-
66
UNIQUE
DETERMINATION
OF
A
DENSITY
FROM
ITS
FRACTIONAL
MOMENTS
-
67
THE
LAPLACE
TRANSFORM
OF
COMPOUND
RANDOM
VARIABLES
-
67
THE
USE
OF
GENERATING
FUNCTIONS
AND
LAPLACE
TRANSFORMS
-
68
EXAMPLES
-
70
NUMERICAL
DETERMINATION
OF
THE
LAPLACE
TRANSFORM
-
72
RECOVERING
A
DENSITY
ON
[0,1]
FROM
ITS
INTEGER
MOMENTS
-
73
COMPUTATION
OF
(6.5)
BY
FOURIER
SUMMATION
-
74
7
7.1
7.2
7.3
7.4
7.4.1
7.4.2
7.5
7.5.1
7.5.2
7.5.3
THE
STANDARD
MAXIMUM
ENTROPY
METHOD
-
76
THE
GENERALIZED
MOMENT
PROBLEM
-
77
THE
ENTROPY
FUNCTION
-
78
THE
MAXIMUM
ENTROPY
METHOD
-
80
TWO
CONCRETE
MODELS
-
82
CASE
1:
THE
FRACTIONAL
MOMENT
PROBLEM
-
82
CASE
2:
GENERIC
CASE
-
82
NUMERICAL
EXAMPLES
-
83
DENSITY
RECONSTRUCTION
FROM
EMPIRICAL
DATA
-
83
RECONSTRUCTION
OF
DENSITIES
AT
SEVERAL
LEVELS
OF
DATA
AGGREGATION
-
87
A
COMPARISON
OF
METHODS
-
95
8
8.1
8.1.1
8.1.2
8.1.3
8.2
8.2.1
EXTENSIONS
OF
THE
METHOD
OF
MAXIMUM
ENTROPY
-
97
GENERALIZED
MOMENT
PROBLEM
WITH
ERRORS
IN
THE
DATA
-
98
THE
BOUNDED
ERROR
CASE
-
98
THE
UNBOUNDED
ERROR
CASE
-
100
THE
FRACTIONAL
MOMENT
PROBLEM
WITH
BOUNDED
MEASUREMENT
ERROR
-
101
GENERALIZED
MOMENT
PROBLEM
WITH
DATA
IN
RANGES
-
102
FRACTIONAL
MOMENT
PROBLEM
WITH
DATA
IN
RANGES
-
104
CONTENTS
-
-
XI
8.3
GENERALIZED
MOMENT
PROBLEM
WITH
ERRORS
IN
THE
DATA
AND
DATA
IN
RANGES
-
105
8.4
8.4.1
8.4.2
NUMERICAL
EXAMPLES
-
106
RECONSTRUCTION
FROM
DATA
IN
INTERVALS
-
107
RECONSTRUCTION
WITH
ERRORS
IN
THE
DATA
-
109
9
9.1
9.2
9.3
9.4
SUPERRESOLUTION
IN
MAXENTROPIC
LAPLACE
TRANSFORM
INVERSION
-
113
INTRODUCTORY
REMARKS
-
113
PROPERTIES
OF
THE
MAXENTROPIC
SOLUTION
-
114
THE
SUPERRESOLUTION
PHENOMENON
-
115
NUMERICAL
EXAMPLE
-
117
10
10.1
10.1.1
10.1.2
10.2
10.2.1
10.3
10.3.1
10.3.2
10.3.3
10.3.4
SAMPLE
DATA
DEPENDENCE
-
119
PRELIMINARIES
-
119
THE
MAXIMUM
ENTROPY
INVERSION
TECHNIQUE
-
120
THE
DEPENDENCE
OF
A
ON
U
-
122
VARIABILITY
OF
THE
RECONSTRUCTIONS
-
123
VARIABILITY
OF
EXPECTED
VALUES
-
127
NUMERICAL
EXAMPLES
-
128
THE
SAMPLE
GENERATION
PROCESS
-
128
THE
'
TRUE
'
MAXENTROPIC
DENSITY
-
129
THE
SAMPLE
DEPENDENCE
OF
THE
MAXENTROPIC
DENSITIES
-
130
COMPUTATION
OF
THE
REGULATORY
CAPITAL
-
134
11
11.1
11.1.1
11.1.2
11.1.3
11.2
11.2.1
11.2.2
DISENTANGLING
FREQUENCIES
AND
DECOMPOUNDING
LOSSES
-
136
DISENTANGLING
THE
FREQUENCIES
-
136
EXAMPLE:
MIXTURES
OF
POISSON
DISTRIBUTIONS
-
138
A
MIXTURE
OF
NEGATIVE
BINOMIALS
-
143
A
MORE
ELABORATE
CASE
-
143
DECOMPOUNDING
THE
LOSSES
-
146
SIMPLE
CASE:
A
MIXTURE
OF
TWO
POPULATIONS
-
148
CASE
2:
SEVERAL
LOSS
FREQUENCIES
WITH
DIFFERENT
INDIVIDUAL
LOSS
DISTRIBUTIONS
-
150
12
12.1
12.1.1
12.1.2
12.1.3
12.2
12.2.1
12.2.2
COMPUTATIONS
USING
THE
MAXENTROPIC
DENSITY
-
152
PRELIMINARY
COMPUTATIONS
-
152
CALCULATING
QUANTILES
OF
COMPOUND
VARIABLES
-
153
CALCULATING
EXPECTED
LOSSES
GIVEN
THAT
THEY
ARE
LARGE
-
154
COMPUTING
THE
QUANTILES
AND
TAIL
EXPECTATIONS
-
154
COMPUTATION
OF
THE
VAR
AND
TVAR
RISK
MEASURES
-
155
SIMPLE
CASE:
A
COMPARISON
TEST
-
155
VAR
AND
TVAR
OF
AGGREGATE
LOSSES
-
158
XII
-
CONTENTS
12.3
COMPUTATION
OF
RISK
PREMIA
-
159
13
A
SOLUTION
TO
THE
CAPITAL
ALLOCATION
PROBLEM
-
162
13.1
INTRODUCTION
AND
PRELIMINARIES
-
162
13.2
NUMERICAL
RESULTS
-
164
13.2.1
THE
CAPITAL
ALLOCATION
-
164
13.2.2
PROBLEM
2:
DETERMINING
THE
DISTORTION
FUNCTION
FROM
GIVEN
RISK
PRICES
-
166
13.3
APPENDICES
-
172
13.3.1
APPLICATION
OF
MEM
TO
DETERMINE
THE
CAPITAL
ALLOCATION
-
172
13.3.2
DISTORTED
RISK
MEASURE
-
175
13.3.3
APPLICATION
OF
MEM
TO
DETERMINE
THE
DISTORTION
MEASURE
-
176
13.3.4
A
NUMERICAL
INSTABILITY
ISSUE
-
177
14
REVIEW
OF
STATISTICAL
PROCEDURES
-
179
14.1
PARAMETER
ESTIMATION
TECHNIQUES
-
179
14.1.1
MAXIMUM
LIKELIHOOD
ESTIMATION
-
179
14.1.2
METHOD
OF
MOMENTS
-
180
14.2
CLUSTERING
METHODS
-
181
14.2.1
K-MEANS
-
181
14.2.2
EM
ALGORITHM
-
182
14.2.3
EM
ALGORITHM
FOR
LINEAR
AND
NONLINEAR
PATTERNS
-
183
14.2.4
EXPLORATORY
PROJECTION
PURSUIT
TECHNIQUES
-
185
14.3
APPROACHES
TO
SELECT
THE
NUMBER
OF
CLUSTERS
-
187
14.3.1
ELBOW
METHOD
-
187
14.3.2
INFORMATION
CRITERIA
APPROACH
-
187
14.3.3
NEGENTROPY
-
188
14.4
VALIDATION
METHODS
FOR
DENSITY
ESTIMATIONS
-
188
14.4.1
GOODNESS
OF
FIT
TEST
FOR
DISCRETE
VARIABLES
-
189
14.4.2
GOODNESS
OF
FIT
TEST
FOR
CONTINUOUS
VARIABLES
-
189
14.4.3
A
NOTE
ABOUT
GOODNESS
OF
FIT
TESTS
-
191
14.4.4
VISUAL
COMPARISONS
-
192
14.4.5
ERROR
MEASUREMENT
-
192
14.5
BEWARE
OF
OVERFITTING
-
193
14.6
COPULAS
-
194
14.6.1
EXAMPLES
OF
COPULAS
-
195
14.6.2
SIMULATION
WITH
COPULAS
-
202
BIBLIOGRAPHY
-
205
INDEX
-
209 |
| adam_txt |
CONTENTS
PREFACE
-
VII
1
1.1
1.2
INTRODUCTION
-
1
THE
BASIC
LOSS
AGGREGATION
PROBLEM
-
1
DESCRIPTION
OF
THE
CONTENTS
-
2
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.2
2.3
2.3.1
2.3.2
FREQUENCY
MODELS
-
5
A
SHORT
LIST
OF
EXAMPLES
-
5
THE
POISSON
DISTRIBUTION
-
6
POISSON
MIXTURES
-
7
THE
NEGATIVE
BINOMIAL
DISTRIBUTION
-
8
BINOMIAL
MODELS
-
9
UNIFIED
VERSION
-
9
EXAMPLES
-
10
DETERMINING
THE
PARAMETER
OF
A
POISSON
DISTRIBUTION
-
11
BINOMIAL
DISTRIBUTION
-
18
3
3.1
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.1.6
3.2
3.2.1
INDIVIDUAL
SEVERITY
MODELS
-
22
A
SHORT
CATALOG
OF
DISTRIBUTIONS
-
22
EXPONENTIAL
DISTRIBUTION
-
22
THE
SIMPLE
PARETO
DISTRIBUTION
-
23
GAMMA
DISTRIBUTION
-
23
THE
LOGNORMAL
DISTRIBUTION
-
24
THE
BETA
DISTRIBUTION
-
24
A
MIXTURE
OF
DISTRIBUTIONS
-
25
NUMERICAL
EXAMPLES
-
25
DATA
FROM
A
DENSITY
-
26
4
4.1
4.2
4.3
4.4
4.5
SOME
DETAILED
EXAMPLES
-
30
CLAIM
DISTRIBUTION
AND
OPERATIONAL
RISK
LOSSES
-
30
SIMPLE
MODEL
OF
CREDIT
RISK
-
31
SHOCK
AND
DAMAGE
MODELS
-
35
BARRIER
CROSSING
TIMES
-
35
APPLICATIONS
IN
RELIABILITY
THEORY
-
36
5
5.1
5.1.1
5.2
5.2.1
SOME
TRADITIONAL
APPROACHES
TO
THE
AGGREGATION
PROBLEM
-
38
GENERAL
REMARKS
-
38
GENERAL
ISSUES
-
39
ANALYTICAL
TECHNIQUES:
THE
MOMENT
GENERATING
FUNCTION
-
40
SIMPLE
EXAMPLES
-
41
X
-
-
CONTENTS
5.3
5.3.1
5.3.2
5.3.3
5.4
5.4.1
5.4.2
5.4.3
5.5
5.6
APPROXIMATE
METHODS
-
44
THE
CASE
OF
COMPUTABLE
CONVOLUTIONS
-
44
SIMPLE
APPROXIMATIONS
TO
THE
TOTAL
LOSS
DISTRIBUTION
-
45
EDGEWORTH
APPROXIMATION
-
46
NUMERICAL
TECHNIQUES
-
48
CALCULATIONS
STARTING
FROM
EMPIRICAL
OR
SIMULATED
DATA
-
48
RECURRENCE
RELATIONS
-
49
FURTHER
NUMERICAL
ISSUES
-
50
NUMERICAL
EXAMPLES
-
50
CONCLUDING
REMARKS
-
60
6
6.1
6.2
6.3
6.4
6.5
6.5.1
6.5.2
6.6
6.6.1
6.6.2
LAPLACE
TRANSFORMS
AND
FRACTIONAL
MOMENT
PROBLEMS
-
62
MATHEMATICAL
PROPERTIES
OF
THE
LAPLACE
TRANSFORM
AND
ITS
INVERSE
-
62
INVERSION
OF
THE
LAPLACE
TRANSFORM
-
64
LAPLACE
TRANSFORM
AND
FRACTIONAL
MOMENTS
-
66
UNIQUE
DETERMINATION
OF
A
DENSITY
FROM
ITS
FRACTIONAL
MOMENTS
-
67
THE
LAPLACE
TRANSFORM
OF
COMPOUND
RANDOM
VARIABLES
-
67
THE
USE
OF
GENERATING
FUNCTIONS
AND
LAPLACE
TRANSFORMS
-
68
EXAMPLES
-
70
NUMERICAL
DETERMINATION
OF
THE
LAPLACE
TRANSFORM
-
72
RECOVERING
A
DENSITY
ON
[0,1]
FROM
ITS
INTEGER
MOMENTS
-
73
COMPUTATION
OF
(6.5)
BY
FOURIER
SUMMATION
-
74
7
7.1
7.2
7.3
7.4
7.4.1
7.4.2
7.5
7.5.1
7.5.2
7.5.3
THE
STANDARD
MAXIMUM
ENTROPY
METHOD
-
76
THE
GENERALIZED
MOMENT
PROBLEM
-
77
THE
ENTROPY
FUNCTION
-
78
THE
MAXIMUM
ENTROPY
METHOD
-
80
TWO
CONCRETE
MODELS
-
82
CASE
1:
THE
FRACTIONAL
MOMENT
PROBLEM
-
82
CASE
2:
GENERIC
CASE
-
82
NUMERICAL
EXAMPLES
-
83
DENSITY
RECONSTRUCTION
FROM
EMPIRICAL
DATA
-
83
RECONSTRUCTION
OF
DENSITIES
AT
SEVERAL
LEVELS
OF
DATA
AGGREGATION
-
87
A
COMPARISON
OF
METHODS
-
95
8
8.1
8.1.1
8.1.2
8.1.3
8.2
8.2.1
EXTENSIONS
OF
THE
METHOD
OF
MAXIMUM
ENTROPY
-
97
GENERALIZED
MOMENT
PROBLEM
WITH
ERRORS
IN
THE
DATA
-
98
THE
BOUNDED
ERROR
CASE
-
98
THE
UNBOUNDED
ERROR
CASE
-
100
THE
FRACTIONAL
MOMENT
PROBLEM
WITH
BOUNDED
MEASUREMENT
ERROR
-
101
GENERALIZED
MOMENT
PROBLEM
WITH
DATA
IN
RANGES
-
102
FRACTIONAL
MOMENT
PROBLEM
WITH
DATA
IN
RANGES
-
104
CONTENTS
-
-
XI
8.3
GENERALIZED
MOMENT
PROBLEM
WITH
ERRORS
IN
THE
DATA
AND
DATA
IN
RANGES
-
105
8.4
8.4.1
8.4.2
NUMERICAL
EXAMPLES
-
106
RECONSTRUCTION
FROM
DATA
IN
INTERVALS
-
107
RECONSTRUCTION
WITH
ERRORS
IN
THE
DATA
-
109
9
9.1
9.2
9.3
9.4
SUPERRESOLUTION
IN
MAXENTROPIC
LAPLACE
TRANSFORM
INVERSION
-
113
INTRODUCTORY
REMARKS
-
113
PROPERTIES
OF
THE
MAXENTROPIC
SOLUTION
-
114
THE
SUPERRESOLUTION
PHENOMENON
-
115
NUMERICAL
EXAMPLE
-
117
10
10.1
10.1.1
10.1.2
10.2
10.2.1
10.3
10.3.1
10.3.2
10.3.3
10.3.4
SAMPLE
DATA
DEPENDENCE
-
119
PRELIMINARIES
-
119
THE
MAXIMUM
ENTROPY
INVERSION
TECHNIQUE
-
120
THE
DEPENDENCE
OF
A
ON
U
-
122
VARIABILITY
OF
THE
RECONSTRUCTIONS
-
123
VARIABILITY
OF
EXPECTED
VALUES
-
127
NUMERICAL
EXAMPLES
-
128
THE
SAMPLE
GENERATION
PROCESS
-
128
THE
'
TRUE
'
MAXENTROPIC
DENSITY
-
129
THE
SAMPLE
DEPENDENCE
OF
THE
MAXENTROPIC
DENSITIES
-
130
COMPUTATION
OF
THE
REGULATORY
CAPITAL
-
134
11
11.1
11.1.1
11.1.2
11.1.3
11.2
11.2.1
11.2.2
DISENTANGLING
FREQUENCIES
AND
DECOMPOUNDING
LOSSES
-
136
DISENTANGLING
THE
FREQUENCIES
-
136
EXAMPLE:
MIXTURES
OF
POISSON
DISTRIBUTIONS
-
138
A
MIXTURE
OF
NEGATIVE
BINOMIALS
-
143
A
MORE
ELABORATE
CASE
-
143
DECOMPOUNDING
THE
LOSSES
-
146
SIMPLE
CASE:
A
MIXTURE
OF
TWO
POPULATIONS
-
148
CASE
2:
SEVERAL
LOSS
FREQUENCIES
WITH
DIFFERENT
INDIVIDUAL
LOSS
DISTRIBUTIONS
-
150
12
12.1
12.1.1
12.1.2
12.1.3
12.2
12.2.1
12.2.2
COMPUTATIONS
USING
THE
MAXENTROPIC
DENSITY
-
152
PRELIMINARY
COMPUTATIONS
-
152
CALCULATING
QUANTILES
OF
COMPOUND
VARIABLES
-
153
CALCULATING
EXPECTED
LOSSES
GIVEN
THAT
THEY
ARE
LARGE
-
154
COMPUTING
THE
QUANTILES
AND
TAIL
EXPECTATIONS
-
154
COMPUTATION
OF
THE
VAR
AND
TVAR
RISK
MEASURES
-
155
SIMPLE
CASE:
A
COMPARISON
TEST
-
155
VAR
AND
TVAR
OF
AGGREGATE
LOSSES
-
158
XII
-
CONTENTS
12.3
COMPUTATION
OF
RISK
PREMIA
-
159
13
A
SOLUTION
TO
THE
CAPITAL
ALLOCATION
PROBLEM
-
162
13.1
INTRODUCTION
AND
PRELIMINARIES
-
162
13.2
NUMERICAL
RESULTS
-
164
13.2.1
THE
CAPITAL
ALLOCATION
-
164
13.2.2
PROBLEM
2:
DETERMINING
THE
DISTORTION
FUNCTION
FROM
GIVEN
RISK
PRICES
-
166
13.3
APPENDICES
-
172
13.3.1
APPLICATION
OF
MEM
TO
DETERMINE
THE
CAPITAL
ALLOCATION
-
172
13.3.2
DISTORTED
RISK
MEASURE
-
175
13.3.3
APPLICATION
OF
MEM
TO
DETERMINE
THE
DISTORTION
MEASURE
-
176
13.3.4
A
NUMERICAL
INSTABILITY
ISSUE
-
177
14
REVIEW
OF
STATISTICAL
PROCEDURES
-
179
14.1
PARAMETER
ESTIMATION
TECHNIQUES
-
179
14.1.1
MAXIMUM
LIKELIHOOD
ESTIMATION
-
179
14.1.2
METHOD
OF
MOMENTS
-
180
14.2
CLUSTERING
METHODS
-
181
14.2.1
K-MEANS
-
181
14.2.2
EM
ALGORITHM
-
182
14.2.3
EM
ALGORITHM
FOR
LINEAR
AND
NONLINEAR
PATTERNS
-
183
14.2.4
EXPLORATORY
PROJECTION
PURSUIT
TECHNIQUES
-
185
14.3
APPROACHES
TO
SELECT
THE
NUMBER
OF
CLUSTERS
-
187
14.3.1
ELBOW
METHOD
-
187
14.3.2
INFORMATION
CRITERIA
APPROACH
-
187
14.3.3
NEGENTROPY
-
188
14.4
VALIDATION
METHODS
FOR
DENSITY
ESTIMATIONS
-
188
14.4.1
GOODNESS
OF
FIT
TEST
FOR
DISCRETE
VARIABLES
-
189
14.4.2
GOODNESS
OF
FIT
TEST
FOR
CONTINUOUS
VARIABLES
-
189
14.4.3
A
NOTE
ABOUT
GOODNESS
OF
FIT
TESTS
-
191
14.4.4
VISUAL
COMPARISONS
-
192
14.4.5
ERROR
MEASUREMENT
-
192
14.5
BEWARE
OF
OVERFITTING
-
193
14.6
COPULAS
-
194
14.6.1
EXAMPLES
OF
COPULAS
-
195
14.6.2
SIMULATION
WITH
COPULAS
-
202
BIBLIOGRAPHY
-
205
INDEX
-
209 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Gzyl, Henryk 1946- Mayoral, Silvia Gomes-Gonçalves, Erika |
| author_GND | (DE-588)172111188 (DE-588)1160062056 (DE-588)116006251X |
| author_facet | Gzyl, Henryk 1946- Mayoral, Silvia Gomes-Gonçalves, Erika |
| author_role | aut aut aut |
| author_sort | Gzyl, Henryk 1946- |
| author_variant | h g hg s m sm e g g egg |
| building | Verbundindex |
| bvnumber | BV048871937 |
| classification_rvk | SK 980 |
| ctrlnum | (OCoLC)1376411576 (DE-599)DNB1274463556 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2nd, extended edition |
| format | Book |
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| id | DE-604.BV048871937 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:44:23Z |
| indexdate | 2024-07-20T03:13:49Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783111047386 3111047385 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034136814 |
| oclc_num | 1376411576 |
| open_access_boolean | |
| owner | DE-92 DE-703 DE-20 |
| owner_facet | DE-92 DE-703 DE-20 |
| physical | XII, 210 Seiten Diagramme 24 cm x 17 cm, 384 g |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter STEM |
| spelling | Gzyl, Henryk 1946- Verfasser (DE-588)172111188 aut Loss data analysis the maximum entropy approach Henryk Gzyl, Silvia Mayoral, and Erika Gomes-Gonçalves 2nd, extended edition Berlin ; Boston De Gruyter [2023] XII, 210 Seiten Diagramme 24 cm x 17 cm, 384 g txt rdacontent n rdamedia nc rdacarrier De Gruyter STEM Risikoanalyse (DE-588)4137042-9 gnd rswk-swf Maximum-Entropie-Methode (DE-588)4277537-1 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Loss probability determination risk aggregation risk disaggregation maximum entropy method Maxentropic Laplace transform inversion. Loss probability determination; risk aggregation; risk disaggregation; maximum entropy method; Maxentropic Laplace transform inversion. Risikoanalyse Datenanalyse TB: Textbook Risikoanalyse (DE-588)4137042-9 s Maximum-Entropie-Methode (DE-588)4277537-1 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Mayoral, Silvia Verfasser (DE-588)1160062056 aut Gomes-Gonçalves, Erika Verfasser (DE-588)116006251X aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-104970-0 Erscheint auch als Online-Ausgabe, PDF 978-3-11-104818-5 X:MVB https://www.degruyter.com/isbn/9783111047386 B:DE-101 application/pdf https://d-nb.info/1274463556/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034136814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20221202 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Gzyl, Henryk 1946- Mayoral, Silvia Gomes-Gonçalves, Erika Loss data analysis the maximum entropy approach Risikoanalyse (DE-588)4137042-9 gnd Maximum-Entropie-Methode (DE-588)4277537-1 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4137042-9 (DE-588)4277537-1 (DE-588)4121894-2 |
| title | Loss data analysis the maximum entropy approach |
| title_auth | Loss data analysis the maximum entropy approach |
| title_exact_search | Loss data analysis the maximum entropy approach |
| title_exact_search_txtP | Loss data analysis the maximum entropy approach |
| title_full | Loss data analysis the maximum entropy approach Henryk Gzyl, Silvia Mayoral, and Erika Gomes-Gonçalves |
| title_fullStr | Loss data analysis the maximum entropy approach Henryk Gzyl, Silvia Mayoral, and Erika Gomes-Gonçalves |
| title_full_unstemmed | Loss data analysis the maximum entropy approach Henryk Gzyl, Silvia Mayoral, and Erika Gomes-Gonçalves |
| title_short | Loss data analysis |
| title_sort | loss data analysis the maximum entropy approach |
| title_sub | the maximum entropy approach |
| topic | Risikoanalyse (DE-588)4137042-9 gnd Maximum-Entropie-Methode (DE-588)4277537-1 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Risikoanalyse Maximum-Entropie-Methode Wahrscheinlichkeitsverteilung |
| url | https://www.degruyter.com/isbn/9783111047386 https://d-nb.info/1274463556/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034136814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gzylhenryk lossdataanalysisthemaximumentropyapproach AT mayoralsilvia lossdataanalysisthemaximumentropyapproach AT gomesgoncalveserika lossdataanalysisthemaximumentropyapproach AT walterdegruytergmbhcokg lossdataanalysisthemaximumentropyapproach |
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