Random errors in observations and the influence of modulation on their distribution:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart
Wittwer
1979
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 151 S. |
| ISBN: | 3879193231 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Random errors in observations and the influence of modulation on their distribution
Autor: Romanowski, M
Jahr: 1979
CONTENTS
Page
Foreword VII
CHAPTER I
fUNDAMENTALS OF THE THEORY OF OBSERVATIONAL ERRORS
BASED ON THE CONCEPT OF ELEMENTARY ERROR
1. Generalities on the samples of repeated observations 1
2. The genesis of the concept of the law of errors 4
3. Outline of Hagen s theory 7
4. Binomial variate 8
5. Hagen s variate and Normal variate 12
6. Fitting a normal curve into an experimentally
obtained diagram 17
7. Numerical examples of the normal distribution 23
8. How large samples originate in practice 29
CHAPTER II
VARIOUS DEVELOPMENTS IN THE THEORY OF BINOMIAL,
NORMAL AND TRINOMIAL VARIATES
1. Introduction. Formula of Stirling 34
2. Further discussion of the binomial variate 35
3. Trinomial variate 39
4. Moments of the normal variate 44
5. The role of the mean 47
6. Combinations of normal variates: summations and mixtures 53
7. Gridgeman s analysis of mixtures 56
8. Some reflexions on the notion of homogeneity 60
CHAPTER III
TREATMENT OF THE LEPTOKURTOSIS BY MEANS
OF THE MODULATION THEORY
1. General introduction to leptokurtosis 63
2. Description of the modulation process 64
3. Modulated normal variate 67
4. Analysis of a few observed samples 72
5. Integration of (a,A) 83
6. Numerical examples 90
7. Characteristic functions 94
8. The role of the Central Limit in MND 97
9. Modulation of Type II 101
10. Integration of functions in Type II 104
11. The top of the modulated normal curve 107
12. Theory of moments in MND 109
CHAPTER IV
FÜRTHER DEVELOPMENTS IN THE THEORY OF MND
1. General foreword 114
2. Convergence of integrals 115
3. Dichotomy 119
4. Dichotomy applied to the summation of variates 125
5. Generalization of Gridgeman s Index (E) 127
6. Modulation of variance 129
7. Chi-square test applied to modulated normal distributions 131
8. Final reflexions on leptokurtosis and modulation 137
BIBLIOGRAPHY
First part 139
Second part 140
Note 141
APPENDIX I:
Tables of modulated normal functions
142
|
| any_adam_object | 1 |
| author | Romanowski, M. |
| author_facet | Romanowski, M. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 511/.43 |
| dewey-search | 511/.43 |
| dewey-sort | 3511 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002084705 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:40:04Z |
| institution | BVB |
| isbn | 3879193231 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001364954 |
| oclc_num | 6302210 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-706 DE-83 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-706 DE-83 DE-188 |
| physical | X, 151 S. |
| psigel | TUB-nveb |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Wittwer |
| record_format | marc |
| spelling | Romanowski, M. Verfasser aut Random errors in observations and the influence of modulation on their distribution by M. Romanowski Stuttgart Wittwer 1979 X, 151 S. txt rdacontent n rdamedia nc rdacarrier Error analysis (Mathematics) Beobachtungsfehler (DE-588)4144588-0 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Beobachtungsfehler (DE-588)4144588-0 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001364954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Romanowski, M. Random errors in observations and the influence of modulation on their distribution Error analysis (Mathematics) Beobachtungsfehler (DE-588)4144588-0 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4144588-0 (DE-588)4121894-2 |
| title | Random errors in observations and the influence of modulation on their distribution |
| title_auth | Random errors in observations and the influence of modulation on their distribution |
| title_exact_search | Random errors in observations and the influence of modulation on their distribution |
| title_full | Random errors in observations and the influence of modulation on their distribution by M. Romanowski |
| title_fullStr | Random errors in observations and the influence of modulation on their distribution by M. Romanowski |
| title_full_unstemmed | Random errors in observations and the influence of modulation on their distribution by M. Romanowski |
| title_short | Random errors in observations and the influence of modulation on their distribution |
| title_sort | random errors in observations and the influence of modulation on their distribution |
| topic | Error analysis (Mathematics) Beobachtungsfehler (DE-588)4144588-0 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Error analysis (Mathematics) Beobachtungsfehler Wahrscheinlichkeitsverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001364954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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