Holdings: Generalized Gaussian error calculus

Generalized Gaussian error calculus: with 47 figures

Saved in:

Bibliographic Details
Main Author:	Grabe, Michael 1939- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2010
Subjects:	Fehlerrechnung
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 301 S. teilw. farb. Ill., graph. Darst.
ISBN:	9783642033049

Staff View

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

Record in the Search Index

_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

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items