Prediction analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a.]
van Nostrand
1967
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 291 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Wolberg, John R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Prediction analysis |c by John R. Wolberg |
| 264 | 1 | |a Princeton, NJ [u.a.] |b van Nostrand |c 1967 | |
| 300 | |a XI, 291 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Voorspelbaarheid |2 gtt | |
| 650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
| 650 | 7 | |a Wiskundige methoden |2 gtt | |
| 650 | 4 | |a Experimental design | |
| 650 | 4 | |a Least squares | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
CHAPTER PAGE
Preface v
PART I
1 INTRODUCTION 3
1.1 The Experimental Method 3
1.2 Planning an Experiment 4
1.3 Definition of Prediction Analysis 5
1.4 Application of Prediction Analysis 6
1.5 Connection with the Method of Least Squares 7
1.6 Scope of the Book 7
2 STATISTICAL BACKGROUND 8
2.1 Introduction 8
2.2 Statistical Frequency 9
2.3 Measures of Location 10
2.4 Measures of Variation 14
2.5 Frequency Distributions 15
2.6 The Uncertainty of a Function of Several Variables 21
Problems 25
3 THE METHOD OF LEAST SQUARES 27
3.1 Introduction 27
3.2 Curve Fitting 28
3.3 General Statement of the Problem 30
3.4 Special Cases of the General Problem 33
3.5 Statistical Weighting 36
3.6 Solution for the General Case 39
3.7 A Specific Application of the Method of Least Squares 45
3.8 Convergence 48
3.9 Solution for the Linear Case 53
3.10 Uncertainties of the Least Squares Parameters 54
3.11 Relative Uncertainties 62
3.12 Confidence Intervals 64
3.13 Goodness of the Fit 68
ix
X CONTENTS
CHAPTER PAGE
3.14 Summary 71
Problems 73
Computer Projects 73
4 PREDICTION ANALYSIS 75
4.1 Introduction 75
4.2 Experimental Uncertainty 75
4.3 Predicting the Values of aaii 76
4.4 The Predicted Elements of the Matrix C 1 78
4.5 An Example of Prediction Analysis—The Straight Line 82
Experiment
4.6 Comparison of Direct and Analytical Solutions 99
4.7 Prediction Analysis and Least Squares Analysis Computer 102
Programs
4.8 Matrix Inversion 111
4.9 Treatment of Systematic Errors 119
4.10 Applying Prediction Analysis to the Optimization of an 126
Experiment
4.11 Summary 132
Problems 134
Computer Projects 135
PART II
5 THE POLYNOMIAL 139
5.1 Introduction 139
5.2 The First Order Polynomial 140
5.3 The Second Order Polynomial 162
5.4 Higher Order Polynomials 175
5.5 Summary 179
Problems 180
Computer Projects 181
6 THE EXPONENTIAL 182
6.1 Introduction 182
6.2 The Simple Exponential 183
6.3 The Exponential Plus Background 197
6.4 Two Exponentials 206
6.5 Exponential with Known Decay Constant 210
6.6 Exponential Plus Background with Known Decay Constant 212
CONTENTS xi
CHAPTER PAGE
6.7 Summary 216
Problems 217
Computer Projects 218
7 THE SINE SERIES 219
7.1 Introduction 219
7.2 The Simple Sine Function 220
7.3 Two Term Sine Series 225
7.4 Three Term Sine Series 230
7.5 Higher Order Sine Series 237
7.6 The Simple Sine Function with Unknown Range 240
7.7 Summary 246
Problems 247
Computer Projects 248
8 THE GAUSSIAN FUNCTION 249
8.1 Introduction 249
8.2 Single Gaussian with Unknown Amplitude 250
8.3 Single Gaussian with Three Unknown Parameters 254
8.4 Two Gaussians with Unknown Amplitudes 261
8.5 Two Gaussians, Each with Three Unknown Parameters 267
8.6 Summary 270
Problems 271
Computer Projects 271
9 APPLYING PREDICTION ANALYSIS TO A 273
COMPLICATED EXPERIMENT
9.1 Introduction 273
9.2 Statement of the Problem 274
9.3 Design of the Experiment 276
9.4 Prediction Analysis of the Proposed Experiment 278
9.5 Results of the Analysis 281
9.6 Conclusions 287
INDEX 289
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:09:25Z |
| institution | BVB |
| language | English |
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| oclc_num | 527107 |
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| owner_facet | DE-91G DE-BY-TUM DE-739 DE-29T DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-706 DE-188 DE-11 |
| physical | XI, 291 S. graph. Darst. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | van Nostrand |
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| spelling | Wolberg, John R. Verfasser aut Prediction analysis by John R. Wolberg Princeton, NJ [u.a.] van Nostrand 1967 XI, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Voorspelbaarheid gtt Waarschijnlijkheidstheorie gtt Wiskundige methoden gtt Experimental design Least squares Statistik (DE-588)4056995-0 gnd rswk-swf Vorhersagetheorie (DE-588)4188671-9 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Vorhersagetheorie (DE-588)4188671-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002601585&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wolberg, John R. Prediction analysis Voorspelbaarheid gtt Waarschijnlijkheidstheorie gtt Wiskundige methoden gtt Experimental design Least squares Statistik (DE-588)4056995-0 gnd Vorhersagetheorie (DE-588)4188671-9 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4188671-9 |
| title | Prediction analysis |
| title_auth | Prediction analysis |
| title_exact_search | Prediction analysis |
| title_full | Prediction analysis by John R. Wolberg |
| title_fullStr | Prediction analysis by John R. Wolberg |
| title_full_unstemmed | Prediction analysis by John R. Wolberg |
| title_short | Prediction analysis |
| title_sort | prediction analysis |
| topic | Voorspelbaarheid gtt Waarschijnlijkheidstheorie gtt Wiskundige methoden gtt Experimental design Least squares Statistik (DE-588)4056995-0 gnd Vorhersagetheorie (DE-588)4188671-9 gnd |
| topic_facet | Voorspelbaarheid Waarschijnlijkheidstheorie Wiskundige methoden Experimental design Least squares Statistik Vorhersagetheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002601585&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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