Stochastic orders:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2007
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Neubearb. von: Shaked, Moshe: Stochastic orders and their applications |
| Physical Description: | XV, 473 S. graph. Darst. |
| ISBN: | 9780387329154 0387329153 |
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MARC
| LEADER | 00000nam a2200000 c 4500 | ||
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| 015 | |a 06,N31,0541 |2 dnb | ||
| 020 | |a 9780387329154 |c Gb. : ca. EUR 74.85 (freier Pr.), ca. sfr 123.50 (freier Pr.) |9 978-0-387-32915-4 | ||
| 020 | |a 0387329153 |c Gb. : ca. EUR 74.85 (freier Pr.), ca. sfr 123.50 (freier Pr.) |9 0-387-32915-3 | ||
| 024 | 3 | |a 9780387329154 | |
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| 100 | 1 | |a Shaked, Moshe |d 1945- |e Verfasser |0 (DE-588)171799925 |4 aut | |
| 245 | 1 | 0 | |a Stochastic orders |c Moshe Shaked ; J. George Shanthikumar |
| 264 | 1 | |a New York, NY |b Springer |c 2007 | |
| 300 | |a XV, 473 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Neubearb. von: Shaked, Moshe: Stochastic orders and their applications | ||
| 650 | 7 | |a Non-parametrische statistiek |2 gtt | |
| 650 | 4 | |a Ordres stochastiques | |
| 650 | 7 | |a Stochastische methoden |2 gtt | |
| 650 | 4 | |a Stochastic orders | |
| 650 | 0 | 7 | |a Stochastische Ordnung |0 (DE-588)4329325-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Shanthikumar, J. George |e Verfasser |0 (DE-588)141320001 |4 aut | |
| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=2835368&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-015656207 | |
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| _version_ | 1805089020362883072 |
|---|---|
| adam_text |
Contents
Univariate
Stochastic
Orders . 3
l.A
The Usual Stochastic Order
. 3
l.A.l Definition
and equivalent conditions
.
З
I.A.2
A characterization by construction on the same
probability space
. 4
1.A.3 Closure properties
. 5
I.A.4
Further characterizations and properties
. 8
I.A.5
Some properties in reliability theory
. 15
l.B The Hazard Rate Order
. 16
l.B.l Definition and equivalent conditions
. 16
l.B.
2
The relation between the hazard rate and the usual
stochastic orders
. 18
1.B.3 Closure properties and some characterizations
. 18
l.B.
4
Comparison of order statistics
. 31
l.B.
5 -
Some properties in reliability theory
. 35
l.B.
6
The reversed hazard order
. 36
l.C The Likelihood Ratio Order
. 42
l.C.l Definition
. 42
l.C.
2
The relation between the likelihood ratio and the
hazard and reversed hazard orders
. 43
1.C.3 Some properties and characterizations
. 44
l.C.
4
Shifted likelihood ratio orders
. 66
l.D The Convolution Order
. 70
l.E Complements
. 71
Mean Residual Life Orders
. 81
2.
A The Mean Residual Life Order
. 81
2.A.1 Definition
. 81
2.
A.
2
The relation between the mean residual life and some
■
other stochastic orders
. 83
2.A.3 Some closure properties
. 86
XII Contents
2.
Α.
4
A property in reliability theory
. 94
2.
В
The Harmonic
Л
lean Residual Life Order
. 94
• 2.
B.I Definition
. 94
2.B.2 The relation between the harmonic mean residual life
and some other stochastic orders
. 95
2.13.3
Some closure properties
. 97
2.B.4 Properties in reliability theory
.105
2.C Complements
.106
3
Univariate Variability Orders
.109
3.Ά
The Convex Order
.109
3.A.1 Definition and equivalent conditions
.109
3.A.2 Closure and other properties
.119
3.A.3 Conditions that lead to the convex order
.133
3.A.4 Some properties in reliability theory
.138
3.A.5 The m-ccmvcx orders
.139
3.B The Dispersive Order
.146
3.B.1 Definition and equivalent conditions
.146
3.B.2 Properties
.151
3.C The Excess Wealth Order
.163
3.C.1 Motivation and definition
.163
3.C.2 Properties
.165
3-D
The Peakedness Order
.171
3.D.1 Definition
.171
3.D.
2
Some properties
.172
3.E Complements
.174
4
Univariate Monotone Convex and Related Orders
.181
4.
A The Monotone Convex and Monotone Concave Orders
.181
4.
A.I Definitions and equivalent conditions
.181
4.
A.
2
Closure properties and some characterizations
.185
4.A.3 Conditions that lead to the increasing convex and
increasing concave orders
.193
4.
A.
4
Further properties
.197
4.
A.
5
Some properties in reliability theory
.203
4.A.
6
The starshaped order
.204
4.
A.
7
Some related orders
.206
4.
В
Transform Orders: Convex, Star, and
Superadditive
Orders
. . . 213
4.B.1 Definitions
.213
4.B.2 Some properties
.214
4.B.3 Some related orders
.221
4.
С
Complements
.227
Contents
ΧΙΠ
The Laplace Transform and Related Orders
.233
5.
A The Laplace Transform Order
.233
5.
A.I, Definitions and equivalent conditions
.233
5.
A.
2
Closure and other properties
.235
б.В
Orders Based on Ratios of Laplace Transforms
.245
5.
B.I Definitions and equivalent conditions
.245
5.B.2 Closure properties
.246
5.B.3 Relationship to other stochastic orders
.249
5.C Some Related Orders
.252
5.
C.I The factorial moments order
.252
Г.
U.C.2 *
The moments order
.255
5.C.3 The moment generating function order
.260
5.
D
Complements
.261
6
Multivariate Stochastic Orders
.265
6.
A Notations and Preliminaries
.265
6.
В
The Usual Multivariate Stochastic Order
.266
6.
B.I Definition and equivalent conditions
.266
6.B.2 A characterization by construction on the same
probability space
.266
6.B.3 Conditions that lead to the multivariate usual
stochastic order
.267
6.B.4 Closure, properties
.273
6.B.5 Further properties
.275
6.B.6 A property in reliability theory
.279
6.B.7 Stochastic ordering of stochastic processes
.280
6.C The Cumulative Hazard Order
.286
6.
C.I Definition
.286
6.C.2 The relationship between the cumulative hazard order
and the usual multivariate stochastic order
.288
6.
D
Multivariate Hazard Rate Orders
.290
6.
D.I Definitions and basic properties
.290
6.D.2- Preservation properties
.292
6.D.3 The dynamic multivariate hazard rate order
.294
6.
Ľ
The Multivariate Likelihood Ratio Order
.298
6.
E.I Definition
.298
6.E.2 Some properties
.298
6.E.3 A property in reliability theory
.304
6.
F
The Multivariate Mean Residual Life Order
.305
r.
G.F.I Definition
.305
6.F.2 The relation between the multivariate mean residual
life and the dynamic multivariate hazard rate orders
. . . 306
6.F.3 A property in reliability theory
.307
6.
G
Other Multivariate Stochastic Orders
.307
6.
G.I The orthant orders
.307
XIV Contents
6.
G.
2
The scaled order statistics orders
.314
6.
H
Complements
.317
7
Multivariate Variability and Related Orders
.323
7.
A The Monotone Convex and Monotone Concave Orders
.323
7.A.1 Definitions
.323
7.
A.
2
Closure properties
.326
7.A.3 Further properties
.328
7.
A.
4
Convex and concave ordering of stochastic processes
. . . 330
7.
A.
5
The (mi
,
m2)-icx orders
.331
7.
A.
6
The symmetric convex order
.332
7.
A.
7
The componentwise convex order
.333
7.
A.
8
The directional convex and concave orders
.335
7.A.9 The orthant convex and concave orders
.339
7.
В
Multivariate Dispersion Orders
.342
7.
B.I A strong multivariate dispersion order
.342
7.B.2 A weak multivariate dispersion order
.344
7.B.3 Dispersive orders based on constructions
.346
7.C Multivariate Transform Orders: Convex, Star, and
Superadditive
Orders
.348
7.
D
The Multivariate Laplace Transform and Related Orders
.349
7.
D.I The multivariate Laplace transform order
.349
7.D.2 The multivariate factorial moments order
.352
7.D.3 The multivariate moments order
.353
7-Е
Complements
.354
8
Stochastic Convexity and Concavity
.357
8.
A Regular Stochastic Convexity
.357
8.A.1 Definitions
.358
8.
A.
2
Closure properties
.362
8.A.3 Stochastic m-convexity
.365
8.B Sample Path Convexity
.367
8.
B.I Definitions
.367
8.B.2 Closure properties
.370
8.
С
Convexity in the Usual Stochastic Order
.374
8.
C.I Definitions
.374
8.C.2 Closure properties
.376
8.
D
Strong Stochastic Convexity
.377
8.
D.I Definitions
.377
8.D.2 Closure properties
.380
8.
E
Stochastic Directional Convexity
.381
8.E.1 Definitions
.381
8.E.2 Closure properties
.382
8.F Complements
.384
Contents XV
9
Positive Dependence Orders
.387
9.
A The PQD and the Supermodular Orders
.387
9.
A.I' Definition and basic properties: The bivariatc case
.387
9.
A.
2
Closure properties
.390
9.A.3 The multivariate ease
.392
9.
A.
4
The supermodular order
.395
9.
В
The Orthant Ratio Orders
.404
9.
B.I The (weak) orthant ratio orders
.404
9.B.
.2
The strong orthant ratio orders
.407
9.C The LTD,
RTL
and
PRD
Orders
.408
9.D The PLRD Order
.414
9.
E
Association Orders
.417
9.F The PDD Order
.420
9.
G
Ordering Exchangeable Distributions
.423
9.
H
Complements
.426
References
.431
Author Index
.459
Subject Index
.467 |
| adam_txt |
Contents
Univariate
Stochastic
Orders . 3
l.A
The Usual Stochastic Order
. 3
l.A.l Definition
and equivalent conditions
.
З
I.A.2
A characterization by construction on the same
probability space
. 4
1.A.3 Closure properties
. 5
I.A.4
Further characterizations and properties
. 8
I.A.5
Some properties in reliability theory
. 15
l.B The Hazard Rate Order
. 16
l.B.l Definition and equivalent conditions
. 16
l.B.
2
The relation between the hazard rate and the usual
stochastic orders
. 18
1.B.3 Closure properties and some characterizations
. 18
l.B.
4
Comparison of order statistics
. 31
l.B.
5 -
Some properties in reliability theory
. 35
l.B.
6
The reversed hazard order
. 36
l.C The Likelihood Ratio Order
. 42
l.C.l Definition
. 42
l.C.
2
The relation between the likelihood ratio and the
hazard and reversed hazard orders
. 43
1.C.3 Some properties and characterizations
. 44
l.C.
4
Shifted likelihood ratio orders
. 66
l.D The Convolution Order
. 70
l.E Complements
. 71
Mean Residual Life Orders
. 81
2.
A The Mean Residual Life Order
. 81
2.A.1 Definition
. 81
2.
A.
2
The relation between the mean residual life and some
■
other stochastic orders
. 83
2.A.3 Some closure properties
. 86
XII Contents
2.
Α.
4
A property in reliability theory
. 94
2.
В
The Harmonic
Л
lean Residual Life Order
. 94
• 2.
B.I Definition
. 94
2.B.2 The relation between the harmonic mean residual life
and some other stochastic orders
. 95
2.13.3
Some closure properties
. 97
2.B.4 Properties in reliability theory
.105
2.C Complements
.106
3
Univariate Variability Orders
.109
3.Ά
The Convex Order
.109
3.A.1 Definition and equivalent conditions
.109
3.A.2 Closure and other properties
.119
3.A.3 Conditions that lead to the convex order
.133
3.A.4 Some properties in reliability theory
.138
3.A.5 The m-ccmvcx orders
.139
3.B The Dispersive Order
.146
3.B.1 Definition and equivalent conditions
.146
3.B.2 Properties
.151
3.C The Excess Wealth Order
.163
3.C.1 Motivation and definition
.163
3.C.2 Properties
.165
3-D
The Peakedness Order
.171
3.D.1 Definition
.171
3.D.
2
Some properties
.172
3.E Complements
.174
4
Univariate Monotone Convex and Related Orders
.181
4.
A The Monotone Convex and Monotone Concave Orders
.181
4.
A.I Definitions and equivalent conditions
.181
4.
A.
2
Closure properties and some characterizations
.185
4.A.3 Conditions that lead to the increasing convex and
increasing concave orders
.193
4.
A.
4
Further properties
.197
4.
A.
5
Some properties in reliability theory
.203
4.A.
6
The starshaped order
.204
4.
A.
7
Some related orders
.206
4.
В
Transform Orders: Convex, Star, and
Superadditive
Orders
. . . 213
4.B.1 Definitions
.213
4.B.2 Some properties
.214
4.B.3 Some related orders
.221
4.
С
Complements
.227
Contents
ΧΙΠ
The Laplace Transform and Related Orders
.233
5.
A The Laplace Transform Order
.233
5.
A.I, Definitions and equivalent conditions
.233
5.
A.
2
Closure and other properties
.235
б.В
Orders Based on Ratios of Laplace Transforms
.245
5.
B.I Definitions and equivalent conditions
.245
5.B.2 Closure properties
.246
5.B.3 Relationship to other stochastic orders
.249
5.C Some Related Orders
.252
5.
C.I The factorial moments order
.252
Г.
U.C.2 *
The moments order
.255
5.C.3 The moment generating function order
.260
5.
D
Complements
.261
6
Multivariate Stochastic Orders
.265
6.
A Notations and Preliminaries
.265
6.
В
The Usual Multivariate Stochastic Order
.266
6.
B.I Definition and equivalent conditions
.266
6.B.2 A characterization by construction on the same
probability space
.266
6.B.3 Conditions that lead to the multivariate usual
stochastic order
.267
6.B.4 Closure, properties
.273
6.B.5 Further properties
.275
6.B.6 A property in reliability theory
.279
6.B.7 Stochastic ordering of stochastic processes
.280
6.C The Cumulative Hazard Order
.286
6.
C.I Definition
.286
6.C.2 The relationship between the cumulative hazard order
and the usual multivariate stochastic order
.288
6.
D
Multivariate Hazard Rate Orders
.290
6.
D.I Definitions and basic properties
.290
6.D.2- Preservation properties
.292
6.D.3 The dynamic multivariate hazard rate order
.294
6.
Ľ
The Multivariate Likelihood Ratio Order
.298
6.
E.I Definition
.298
6.E.2 Some properties
.298
6.E.3 A property in reliability theory
.304
6.
F
The Multivariate Mean Residual Life Order
.305
r.
G.F.I Definition
.305
6.F.2 The relation between the multivariate mean residual
life and the dynamic multivariate hazard rate orders
. . . 306
6.F.3 A property in reliability theory
.307
6.
G
Other Multivariate Stochastic Orders
.307
6.
G.I The orthant orders
.307
XIV Contents
6.
G.
2
The scaled order statistics orders
.314
6.
H
Complements
.317
7
Multivariate Variability and Related Orders
.323
7.
A The Monotone Convex and Monotone Concave Orders
.323
7.A.1 Definitions
.323
7.
A.
2
Closure properties
.326
7.A.3 Further properties
.328
7.
A.
4
Convex and concave ordering of stochastic processes
. . . 330
7.
A.
5
The (mi
,
m2)-icx orders
.331
7.
A.
6
The symmetric convex order
.332
7.
A.
7
The componentwise convex order
.333
7.
A.
8
The directional convex and concave orders
.335
7.A.9 The orthant convex and concave orders
.339
7.
В
Multivariate Dispersion Orders
.342
7.
B.I A strong multivariate dispersion order
.342
7.B.2 A weak multivariate dispersion order
.344
7.B.3 Dispersive orders based on constructions
.346
7.C Multivariate Transform Orders: Convex, Star, and
Superadditive
Orders
.348
7.
D
The Multivariate Laplace Transform and Related Orders
.349
7.
D.I The multivariate Laplace transform order
.349
7.D.2 The multivariate factorial moments order
.352
7.D.3 The multivariate moments order
.353
7-Е
Complements
.354
8
Stochastic Convexity and Concavity
.357
8.
A Regular Stochastic Convexity
.357
8.A.1 Definitions
.358
8.
A.
2
Closure properties
.362
8.A.3 Stochastic m-convexity
.365
8.B Sample Path Convexity
.367
8.
B.I Definitions
.367
8.B.2 Closure properties
.370
8.
С
Convexity in the Usual Stochastic Order
.374
8.
C.I Definitions
.374
8.C.2 Closure properties
.376
8.
D
Strong Stochastic Convexity
.377
8.
D.I Definitions
.377
8.D.2 Closure properties
.380
8.
E
Stochastic Directional Convexity
.381
8.E.1 Definitions
.381
8.E.2 Closure properties
.382
8.F Complements
.384
Contents XV
9
Positive Dependence Orders
.387
9.
A The PQD and the Supermodular Orders
.387
9.
A.I' Definition and basic properties: The bivariatc case
.387
9.
A.
2
Closure properties
.390
9.A.3 The multivariate ease
.392
9.
A.
4
The supermodular order
.395
9.
В
The Orthant Ratio Orders
.404
9.
B.I The (weak) orthant ratio orders
.404
9.B.
.2
The strong orthant ratio orders
.407
9.C The LTD,
RTL
and
PRD
Orders
.408
9.D The PLRD Order
.414
9.
E
Association Orders
.417
9.F The PDD Order
.420
9.
G
Ordering Exchangeable Distributions
.423
9.
H
Complements
.426
References
.431
Author Index
.459
Subject Index
.467 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Shaked, Moshe 1945- Shanthikumar, J. George |
| author_GND | (DE-588)171799925 (DE-588)141320001 |
| author_facet | Shaked, Moshe 1945- Shanthikumar, J. George |
| author_role | aut aut |
| author_sort | Shaked, Moshe 1945- |
| author_variant | m s ms j g s jg jgs |
| building | Verbundindex |
| bvnumber | BV022448275 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.6 |
| callnumber-search | QA273.6 |
| callnumber-sort | QA 3273.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 820 |
| classification_tum | MAT 622f |
| ctrlnum | (OCoLC)76835043 (DE-599)BVBBV022448275 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV022448275 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:35:23Z |
| indexdate | 2024-07-20T09:17:16Z |
| institution | BVB |
| isbn | 9780387329154 0387329153 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015656207 |
| oclc_num | 76835043 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM DE-521 DE-11 DE-824 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-M382 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM DE-521 DE-11 DE-824 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-M382 |
| physical | XV, 473 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Shaked, Moshe 1945- Verfasser (DE-588)171799925 aut Stochastic orders Moshe Shaked ; J. George Shanthikumar New York, NY Springer 2007 XV, 473 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Neubearb. von: Shaked, Moshe: Stochastic orders and their applications Non-parametrische statistiek gtt Ordres stochastiques Stochastische methoden gtt Stochastic orders Stochastische Ordnung (DE-588)4329325-6 gnd rswk-swf Stochastische Ordnung (DE-588)4329325-6 s DE-604 Shanthikumar, J. George Verfasser (DE-588)141320001 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2835368&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015656207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shaked, Moshe 1945- Shanthikumar, J. George Stochastic orders Non-parametrische statistiek gtt Ordres stochastiques Stochastische methoden gtt Stochastic orders Stochastische Ordnung (DE-588)4329325-6 gnd |
| subject_GND | (DE-588)4329325-6 |
| title | Stochastic orders |
| title_auth | Stochastic orders |
| title_exact_search | Stochastic orders |
| title_exact_search_txtP | Stochastic orders |
| title_full | Stochastic orders Moshe Shaked ; J. George Shanthikumar |
| title_fullStr | Stochastic orders Moshe Shaked ; J. George Shanthikumar |
| title_full_unstemmed | Stochastic orders Moshe Shaked ; J. George Shanthikumar |
| title_short | Stochastic orders |
| title_sort | stochastic orders |
| topic | Non-parametrische statistiek gtt Ordres stochastiques Stochastische methoden gtt Stochastic orders Stochastische Ordnung (DE-588)4329325-6 gnd |
| topic_facet | Non-parametrische statistiek Ordres stochastiques Stochastische methoden Stochastic orders Stochastische Ordnung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2835368&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015656207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shakedmoshe stochasticorders AT shanthikumarjgeorge stochasticorders |