A mathematical model for grouped extreme values with an application in automotive engineering:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Stuttgart
Fraunhofer Verl.
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 240 S. graph. Darst. 210 mm x 148 mm |
| ISBN: | 9783839607015 3839607019 |
Internformat
MARC
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| 245 | 1 | 0 | |a A mathematical model for grouped extreme values with an application in automotive engineering |c Sebastian Seifen |
| 264 | 1 | |a Stuttgart |b Fraunhofer Verl. |c 2014 | |
| 300 | |a XV, 240 S. |b graph. Darst. |c 210 mm x 148 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Zugl.: Kaiserslautern, Techn. Univ., Diss., 2013 | ||
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| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027583255 | ||
Datensatz im Suchindex
| _version_ | 1804152629709766656 |
|---|---|
| adam_text | CONTENTS
LIST OF TABLES IX
LIST OF FIGURES XI
TABLE OF ABBREVIATIONS AND SYMBOLS XIII
1 PREFACE 1
2 MOTIVATION, PROBLEM STATEMENT AND METHODS 3
2.1 SOLE - SUPRA OPERATING LOAD EVENT 3
2.2 EXPERIMENTAL DESIGN 4
2.3 MAIN GOALS AND APPROACH 5
2.4 METHODS 7
2.4.1 CHARACTERISTICS OF RANDOM VARIABLES 7
2.4.2 STATISTICAL EXPERIMENT AND LIKELIHOOD FUNCTION 8
2.4.3 FISHER INFORMATION AND UNBIASED, CONSISTENT AND EFFICIENT
ESTIMATORS 8
2.4.4 MAXIMUM LIKELIHOOD METHOD 10
2.4.5 DISTRIBUTIONS 10
2.4.6 CUMULANTS 13
2.4.7 EXTREME VALUE THEORY 14
3 A MODEL FOR SUPRA OPERATING LOAD EVENTS 19
3.1 SOLES IN MATHEMATICAL TERMINOLOGY 19
3.2 DISTRIBUTION OF COUNTS PER RANGE AND MILEAGE 22
3.3 (IN-)DEPENDENCE OF NUMBER OF SOLES IN DISJOINT RANGES 29
3.4 INCLUDING THE MAXIMUM SOLE 32
3.5 SELECTING THE DISTRIBUTION OF NUMBER OF SOLES PER KILOMETER . . 36
3.5.1 THE INDEX OF DISPERSION 37
3.5.2 CONFIDENCE INTERVALS OF SAMPLE INDEX OF DISPERSION .... 40
3.5.3 HYPOTHESIS TEST FOR POISSON APPROACH 45
3.5.4 OVERDISPERSION 46
HTTP://D-NB.INFO/1050661885
VI
CONTENTS
3.5.5 UNDERDISPERSION 48
3.5.6 BINOMIAL, POISSON AND NEGATIVE BINOMIAL APPROACH FOR
HIGH MILEAGES 48
3.5.7 CONCLUSION 52
3.6 SELECTING THE DISTRIBUTION OF SEVERITY OF SOLES 53
4 PARAMETER ESTIMATION 55
4.1 PRELIMINARY . . 55
4.2 STATISTICAL EXPERIMENT 57
4.2.1 COUNTING MODEL 57
4.2.2 COUNTING-MAXIMUM MODEL 59
4.2.3 LOG-LIKELIHOOD FUNCTIONS 59
4.2.4 FISHER INFORMATION OF THE COUNTING MODEL 61
4.3 ESTIMATING THE NUMBER OF SOLES PER KILOMETER 70
4.3.1 ESTIMATING THE MEAN FI OF THE NUMBER OF SOLES PER KILO
METER 72
4.3.2 ESTIMATING THE EXPONENT G OF THE NUMBER OF SOLES PER
KILOMETER 80
4.4 ESTIMATING THE SEVERITY OF A SOLE IN THE COUNTING MODEL .... 87
4.4.1 WHEN DOES THE MAXIMUM LIKELIHOOD ESTIMATOR OF (, /3)
NOT EXIST 87
4.4.2 MAXIMUM LIKELIHOOD ESTIMATION OF (. J8) 90
4.4.3 CONFIDENCE INTERVALS 101
4.4.4 EQUIDISTANT CLASS LIMITS AND OPTIMAL CLASS LENGTH . . . 103
4.5 ESTIMATING THE SEVERITY OF A SOLE IN THE COUNTING-MAXIMUM
MODEL 110
5 IMPLEMENTATION AND RESULTS 117
5.1 GENERATING RANDOM SAMPLES 117
5.1.1 SAMPLES FROM ZI
T
A 118
5.1.2 SAMPLES FROM (ZJ./IJ,..., 118
5.1.3 SAMPLES FROM M
S
*E
V
119
5.1.4 SAMPLES FROM (M
S
*
E
V
, ZI^,..., ZI
T
A
D
) 121
5.2 ACCURACY AND POWER OF INDEX-OF-DISPERSION HYPOTHESIS TEST . . . 122
5.2.1 ACCURACY 123
5.2.2 POWER 124
5.3 CALCULATION AND ACCURACY OF MAXIMUM LIKELIHOOD ESTIMATOR OF G 127
5.3.1 CALCULATION 127
5.3.2 ACCURACY 129
5.4 ACCURACY OF MAXIMUM LIKELIHOOD ESTIMATOR OF /X 131
5.5 CALCULATION AND ACCURACY OF MLE OF (,/3) IN C 132
5.5.1 CALCULATION 132
5.5.2 ACCURACY IN CASE OF * LR O 135
CONTENTS VII
5.5.3 ACCURACY IN CASE OF = 0 136
5.5.4 OPTIMAL CLASS LIMITS 138
5.5.5 COMPARISON WITH UNCENSORED GENERALIZED PARETO MODEL . 142
5.6 CALCULATION AND ACCURACY OF MLE OF (,
0) IN
CM
144
5.6.1 CALCULATION 144
5.6.2 ACCURACY 145
5.7 RESULTS OF MEASUREMENT STUDY 146
6 R6SUM6 155
A LEMMATA 157
B TABLES 175
C FIGURES 205
BIBLIOGRAPHY 229
INDEX 237
|
| any_adam_object | 1 |
| author | Seifen, Sebastian 1985- |
| author_GND | (DE-588)1051112893 |
| author_facet | Seifen, Sebastian 1985- |
| author_role | aut |
| author_sort | Seifen, Sebastian 1985- |
| author_variant | s s ss |
| building | Verbundindex |
| bvnumber | BV042143323 |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)881358319 (DE-599)DNB1050661885 |
| 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 |
| format | Thesis Book |
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| id | DE-604.BV042143323 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:13:45Z |
| institution | BVB |
| isbn | 9783839607015 3839607019 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027583255 |
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| physical | XV, 240 S. graph. Darst. 210 mm x 148 mm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Fraunhofer Verl. |
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| spelling | Seifen, Sebastian 1985- Verfasser (DE-588)1051112893 aut A mathematical model for grouped extreme values with an application in automotive engineering Sebastian Seifen Stuttgart Fraunhofer Verl. 2014 XV, 240 S. graph. Darst. 210 mm x 148 mm txt rdacontent n rdamedia nc rdacarrier Zugl.: Kaiserslautern, Techn. Univ., Diss., 2013 Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Extremwertstatistik (DE-588)4153429-3 gnd rswk-swf Poisson-Verteilung (DE-588)4253010-6 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Parametrisches Verfahren (DE-588)4205938-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Extremwertstatistik (DE-588)4153429-3 s Parametrisches Verfahren (DE-588)4205938-0 s Statistischer Test (DE-588)4077852-6 s Poisson-Verteilung (DE-588)4253010-6 s Maximum-Likelihood-Schätzung (DE-588)4194624-8 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027583255&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seifen, Sebastian 1985- A mathematical model for grouped extreme values with an application in automotive engineering Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Extremwertstatistik (DE-588)4153429-3 gnd Poisson-Verteilung (DE-588)4253010-6 gnd Statistischer Test (DE-588)4077852-6 gnd Parametrisches Verfahren (DE-588)4205938-0 gnd |
| subject_GND | (DE-588)4194624-8 (DE-588)4240945-7 (DE-588)4153429-3 (DE-588)4253010-6 (DE-588)4077852-6 (DE-588)4205938-0 (DE-588)4113937-9 |
| title | A mathematical model for grouped extreme values with an application in automotive engineering |
| title_auth | A mathematical model for grouped extreme values with an application in automotive engineering |
| title_exact_search | A mathematical model for grouped extreme values with an application in automotive engineering |
| title_full | A mathematical model for grouped extreme values with an application in automotive engineering Sebastian Seifen |
| title_fullStr | A mathematical model for grouped extreme values with an application in automotive engineering Sebastian Seifen |
| title_full_unstemmed | A mathematical model for grouped extreme values with an application in automotive engineering Sebastian Seifen |
| title_short | A mathematical model for grouped extreme values with an application in automotive engineering |
| title_sort | a mathematical model for grouped extreme values with an application in automotive engineering |
| topic | Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Extremwertstatistik (DE-588)4153429-3 gnd Poisson-Verteilung (DE-588)4253010-6 gnd Statistischer Test (DE-588)4077852-6 gnd Parametrisches Verfahren (DE-588)4205938-0 gnd |
| topic_facet | Maximum-Likelihood-Schätzung Monte-Carlo-Simulation Extremwertstatistik Poisson-Verteilung Statistischer Test Parametrisches Verfahren Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027583255&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT seifensebastian amathematicalmodelforgroupedextremevalueswithanapplicationinautomotiveengineering |