# Generalized Gaussian Error Calculus

• Michael Grabe
Book

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

### 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