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Generalized Gaussian Error Calculus

  • Michael Grabe

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Basics of Metrology

    1. Front Matter
      Pages 1-1
    2. Michael Grabe
      Pages 3-8
    3. Michael Grabe
      Pages 9-21
  3. Generalized Gaussian Error Calculus

    1. Front Matter
      Pages 23-23
    2. Michael Grabe
      Pages 25-29
    3. Michael Grabe
      Pages 31-33
    4. Michael Grabe
      Pages 35-36
  4. Error Propagation

    1. Front Matter
      Pages 37-37
    2. Michael Grabe
      Pages 39-52
    3. Michael Grabe
      Pages 53-78
    4. Michael Grabe
      Pages 79-88
  5. Essence of Metrology

    1. Front Matter
      Pages 89-89
    2. Michael Grabe
      Pages 91-100
    3. Michael Grabe
      Pages 101-112
    4. Michael Grabe
      Pages 113-114
  6. Fitting of Straight Lines

    1. Front Matter
      Pages 115-115
    2. Michael Grabe
      Pages 117-119
    3. Michael Grabe
      Pages 121-129
    4. Michael Grabe
      Pages 131-140
    5. Michael Grabe
      Pages 141-152
  7. Fitting of Planes

    1. Front Matter
      Pages 153-153
    2. Michael Grabe
      Pages 155-156
    3. Michael Grabe
      Pages 157-163
    4. Michael Grabe
      Pages 165-177
    5. Michael Grabe
      Pages 179-190
  8. Fitting of Parabolas

    1. Front Matter
      Pages 191-191
    2. Michael Grabe
      Pages 193-194
    3. Michael Grabe
      Pages 195-201
    4. Michael Grabe
      Pages 203-212
    5. Michael Grabe
      Pages 213-224
  9. Non-linear Fitting

    1. Front Matter
      Pages 225-225
    2. Michael Grabe
      Pages 227-235
    3. Michael Grabe
      Pages 237-242
  10. Back Matter
    Pages 243-301

About this book

Introduction

For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large.

The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions.

The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence interval as put down by Student, and a contribution due to unknown systematic errors, as expressed by an appropriate worst case estimation.

Keywords

Gaussian error calculus Generalized error calculus Random errors in measurements Systematic errors in measurements Theory of error calculation mathematics

Authors and affiliations

  • Michael Grabe
    • 1
  1. 1.BraunschweigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-03305-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-03304-9
  • Online ISBN 978-3-642-03305-6
  • Buy this book on publisher's site