Grabe M. Generalized Gaussian Error Calculus

Berlin: Springer, 2010. — 301 p.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.True Values and Traceability
Models and ApproachesThe New Uncertainties
Treatment of Random Errors
Treatment of Systematic ErrorsMeans and Means of Means
Functions of Erroneous Variables
Method of Least SquaresDissemination of Units
Multiples and Sub-multiples
Founding PillarsPreliminaries
Straight Lines: Case (i)
Straight Lines: Case (ii)
Straight Lines: Case (iii)Preliminaries
Planes: Case (i)
Planes: Case (ii)
Planes: Case (iii)Preliminaries
Parabolas: Case (i)
Parabolas: Case (ii)
Parabolas: Case (iii)Series Truncation
Transformation