Generalized Gaussian error calculus: with 47 figures
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 301 S. teilw. farb. Ill., graph. Darst. |
| ISBN: | 9783642033049 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV036426682 | ||
| 003 | DE-604 | ||
| 005 | 20120911 | ||
| 007 | t | ||
| 008 | 100428s2010 gw ad|| |||| 00||| eng d | ||
| 016 | 7 | |a 99533837X |2 DE-101 | |
| 020 | |a 9783642033049 |9 978-3-642-03304-9 | ||
| 035 | |a (OCoLC)612366839 | ||
| 035 | |a (DE-599)DNB99533837X | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-11 |a DE-19 |a DE-83 |a DE-824 | ||
| 082 | 0 | |a 530.8 |2 22/ger | |
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 084 | |a SK 910 |0 (DE-625)143270: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a 530 |2 sdnb | ||
| 100 | 1 | |a Grabe, Michael |d 1939- |e Verfasser |0 (DE-588)106779591 |4 aut | |
| 245 | 1 | 0 | |a Generalized Gaussian error calculus |b with 47 figures |c Michael Grabe |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XIII, 301 S. |b teilw. farb. Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Fehlerrechnung |0 (DE-588)4153837-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fehlerrechnung |0 (DE-588)4153837-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-03305-6 |
| 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=020299365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020299365 | ||
Datensatz im Suchindex
| _version_ | 1804142902116352000 |
|---|---|
| adam_text | CONTENTS PART I BASICS OF METROLOGY 1 TRUE VALUES AND TRACEABILITY 3 1.1
METROLOGY 3 1.2 TRACEABILITY 3 1.3 MEASUREMENT ERRORS 4 1.4 PRECISION
AND ACCURACY 6 1.5 MEASUREMENT UNCERTAINTY 6 1.6 MEASURING RESULT 6 1.7
RIVALING PHYSICAL APPROACHES 8 2 MODELS AND APPROACHES 9 2.1 GAUSSIAN
ERROR MODEL 9 2.2 GENERALIZED GAUSSIAN APPROACH 10 2.3 ROBUST TESTING
CONDITIONS 14 2.4 LINEARIZATIONS 15 2.5 QUIDDITY OF LEAST SQUARES 16 2.6
ANALYSIS OF VARIANCE 20 2.7 ROAD MAP 21 PART II GENERALIZED GAUSSIAN
ERROR CALCULUS 3 THE NEW UNCERTAINTIES 25 3.1 GAUSSIAN VERSUS
GENERALIZED GAUSSIAN APPROACH 25 3.2 UNCERTAINTY AND TRUE VALUE 25 3.3
DESIGNING UNCERTAINTIES 26 3.4 QUASI SAFENESS 29 4 TREATMENT OF RANDOM
ERRORS 31 4.1 WELL-DEFINED MEASURING CONDITIONS 31 4.2 MULTIDIMENSIONAL
NORMAL MODEL 32 4.3 PERMUTATION OF REPEATED MEASUREMENTS 33
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/99533837X DIGITALISIERT
DURCH X CONTENTS 5 TREATMENT OF SYSTEMATIC ERRORS 35 5.1 REPERCUSSION OF
BIASES 35 5.2 UNIQUENESS OF WORST-CASE ASSESSMENTS 36 PART III ERROR
PROPAGATION 6 MEANS AND MEANS OF MEANS 39 6.1 ARITHMETIC MEAN 39 6.2
EXTRAVAGATED AVERAGES 41 6.3 MEAN OF MEANS 41 6.4 INDIVIDUAL MEAN VERSUS
GRAND MEAN 47 7 FUNCTIONS OF ERRONEOUS VARIABLES 53 7.1 ONE VARIABLE 53
7.2 TWO VARIABLES 56 7.3 MORE THAN TWO VARIABLES 61 7.4 CONCATENATED
FUNCTIONS 66 7.5 ELEMENTARY EXAMPLES 68 7.6 TEST OF HYPOTHESIS 74 8
METHOD OF LEAST SQUARES 79 8.1 EMPIRICAL VARIANCE*COVARIANCE MATRIX 79
8.2 PROPAGATION OF SYSTEMATIC ERRORS 82 8.3 UNCERTAINTIES OF THE
ESTIMATORS 83 8.4 WEIGHTING FACTORS 84 8.5 EXAMPLE 87 PART IV ESSENCE OF
METROLOGY 9 DISSEMINATION OF UNITS 91 9.1 WORKING STANDARDS 91 9.2 KEY
COMPARISONS 95 10 MULTIPLES AND SUB-MULTIPLES 101 10.1 CALIBRATION
CHAINS 101 10.2 PAIRWISE COMPARISONS 110 11 FOUNDING PILLARS 113 11.1
CONSISTENCY 113 11.2 TRACEABILITY 114 17.5 PC-REGION 161 CONTENTS XI
PART V FITTING OF STRAIGHT LINES 12 PRELIMINARIES 117 12.1 DISTINCTION
OF CASES 117 12.2 TRUE STRAIGHT LINE 118 13 STRAIGHT LINES: CASE (I) 121
13.1 FITTING CONDITIONS 121 13.2 ORTHOGONAL PROJECTION 121 13.3
UNCERTAINTIES OF THE INPUT DATA 123 13.4 UNCERTAINTIES OF THE COMPONENTS
OF THE SOLUTION VECTOR 124 13.5 UNCERTAINTY BAND 126 13.6 SP-REGION 127
14 STRAIGHT LINES: CASE (II) 131 14.1 FITTING CONDITIONS 131 14.2
ORTHOGONAL PROJECTION 132 14.3 UNCERTAINTIES OF THE COMPONENTS OF THE
SOLUTION VECTOR 132 14.4 UNCERTAINTY BAND 135 14.5 P-REGION 137 15
STRAIGHT LINES: CASE (III) 141 15.1 FITTING CONDITIONS 141 15.2
ORTHOGONAL PROJECTION 142 15.3 SERIES EXPANSION OF THE SOLUTION VECTOR
143 15.4 UNCERTAINTIES OF THE COMPONENTS OF THE SOLUTION VECTOR 145 15.5
UNCERTAINTY BAND 147 15.6 P-REGION 148 PART VI FITTING OF PLANES 16
PRELIMINARIES 155 16.1 DISTINCTION OF CASES 155 16.2 TRUE PLANE 155 17
PLANES: CASE (I) 157 17.1 FITTING CONDITIONS 157 17.2 ORTHOGONAL
PROJECTION 157 17.3 UNCERTAINTIES OF THE INPUT DATA 158 17.4
UNCERTAINTIES OF THE COMPONENTS OF THE SOLUTION VECTOR 159 XII CONTENTS
18 PLANES: CASE (II) 165 18.1 FITTING CONDITIONS 165 18.2 ORTHOGONAL
PROJECTION 166 18.3 UNCERTAINTIES OF THE COMPONENTS OF THE SOLUTION
VECTOR 166 18.4 CONFIDENCE INTERVALS AND OVERALL UNCERTAINTIES 168 18.5
UNCERTAINTY BOWLS 169 18.6 PC-REGION 171 19 PLANES: CASE (III) 179
19.1 FITTING CONDITIONS 179 19.2 ORTHOGONAL PROJECTION 180 19.3 SERIES
EXPANSION OF THE SOLUTION VECTOR 181 19.4 UNCERTAINTIES OF THE
COMPONENTS OF THE SOLUTION VECTOR 183 19.5 UNCERTAINTY BOWLS 185 19.6
PC-REGION 187 PART VII FITTING OF PARABOLAS 20 PRELIMINARIES 193 20.1
DISTINCTION OF CASES 193 20.2 TRUE PARABOLA 193 21 PARABOLAS: CASE (I)
195 21.1 FITTING CONDITIONS 195 21.2 ORTHOGONAL PROJECTION 195 21.3
UNCERTAINTIES OF THE INPUT DATA 196 21.4 UNCERTAINTIES OF THE COMPONENTS
OF THE SOLUTION VECTOR 197 21.5 UNCERTAINTY BAND 199 21.6 PC-REGION
199 22 PARABOLAS: CASE (II) 203 22.1 FITTING CONDITIONS 203 22.2
ORTHOGONAL PROJECTION 204 22.3 UNCERTAINTIES OF THE COMPONENTS OF THE
SOLUTION VECTOR 204 22.4 UNCERTAINTY BAND 207 22.5 PC-REGION 209 23
PARABOLAS: CASE (III) 213 23.1 FITTING CONDITIONS 213 23.2 ORTHOGONAL
PROJECTION 214 23. 299 CONTENTS XIII PART VIII NON-LINEAR FITTING 24
SERIES TRUNCATION 227 24.1 HOMOLOGOUS TRUE FUNCTION 227 24.2 FITTING
CONDITIONS 228 24.3 ORTHOGONAL PROJECTION 228 24.4 ITERATION 230 24.5
UNCERTAINTIES OF THE COMPONENTS OF THE SOLUTION VECTOR 231 25
TRANSFORMATION 237 25.1 HOMOLOGOUS TRUE FUNCTION 237 25.2 FITTING
CONDITIONS 237 25.3 ORTHOGONAL PROJECTION 238 25.4 UNCERTAINTIES OF THE
COMPONENTS OF THE SOLUTION VECTOR 239 PART IX APPENDICES A GRAPHICAL
SCALE TRANSFORMATIONS 245 B EXPANSION OF SOLUTION VECTORS 251 C SPECIAL
CONFIDENCE ELLIPSES AND ELLIPSOIDS 257 D EXTREME POINTS OF ELLIPSES AND
ELLIPSOIDS 261 E DRAWING ELLIPSES AND ELLIPSOIDS 265 F SECURITY POLYGONS
AND POLYHEDRA 267 G EP BOUNDARIES AND EPC HULLS 277 H STUDENT S DENSITY
283 I UNCERTAINTY BAND VERSUS EP-REGION 287 J QUANTILES OF HOTELLING S
DENSITY 295 REFERENCES 297 INDEX
|
| any_adam_object | 1 |
| author | Grabe, Michael 1939- |
| author_GND | (DE-588)106779591 |
| author_facet | Grabe, Michael 1939- |
| author_role | aut |
| author_sort | Grabe, Michael 1939- |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV036426682 |
| classification_rvk | SK 800 SK 910 |
| ctrlnum | (OCoLC)612366839 (DE-599)DNB99533837X |
| dewey-full | 530.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.8 |
| dewey-search | 530.8 |
| dewey-sort | 3530.8 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01485nam a2200397 c 4500</leader><controlfield tag="001">BV036426682</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20120911 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100428s2010 gw ad|| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">99533837X</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642033049</subfield><subfield code="9">978-3-642-03304-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)612366839</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB99533837X</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-11</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.8</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 800</subfield><subfield code="0">(DE-625)143256:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 910</subfield><subfield code="0">(DE-625)143270:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">530</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Grabe, Michael</subfield><subfield code="d">1939-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)106779591</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generalized Gaussian error calculus</subfield><subfield code="b">with 47 figures</subfield><subfield code="c">Michael Grabe</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 301 S.</subfield><subfield code="b">teilw. farb. Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fehlerrechnung</subfield><subfield code="0">(DE-588)4153837-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Fehlerrechnung</subfield><subfield code="0">(DE-588)4153837-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-642-03305-6</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020299365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020299365</subfield></datafield></record></collection> |
| id | DE-604.BV036426682 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:39:08Z |
| institution | BVB |
| isbn | 9783642033049 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020299365 |
| oclc_num | 612366839 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM DE-83 DE-824 |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-83 DE-824 |
| physical | XIII, 301 S. teilw. farb. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| spelling | Grabe, Michael 1939- Verfasser (DE-588)106779591 aut Generalized Gaussian error calculus with 47 figures Michael Grabe Berlin [u.a.] Springer 2010 XIII, 301 S. teilw. farb. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fehlerrechnung (DE-588)4153837-7 gnd rswk-swf Fehlerrechnung (DE-588)4153837-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-03305-6 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020299365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grabe, Michael 1939- Generalized Gaussian error calculus with 47 figures Fehlerrechnung (DE-588)4153837-7 gnd |
| subject_GND | (DE-588)4153837-7 |
| title | Generalized Gaussian error calculus with 47 figures |
| title_auth | Generalized Gaussian error calculus with 47 figures |
| title_exact_search | Generalized Gaussian error calculus with 47 figures |
| title_full | Generalized Gaussian error calculus with 47 figures Michael Grabe |
| title_fullStr | Generalized Gaussian error calculus with 47 figures Michael Grabe |
| title_full_unstemmed | Generalized Gaussian error calculus with 47 figures Michael Grabe |
| title_short | Generalized Gaussian error calculus |
| title_sort | generalized gaussian error calculus with 47 figures |
| title_sub | with 47 figures |
| topic | Fehlerrechnung (DE-588)4153837-7 gnd |
| topic_facet | Fehlerrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020299365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT grabemichael generalizedgaussianerrorcalculuswith47figures |