Springer Generalized Gaussian Error Calculus

This book addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. It integrates mathematics and its applications to physical measurements, and serves as a text for graduate students and a reference for researchers. Review From the reviews:“This book is aimed at the metrology community. … The approach elaborated in this book assesses unknown systematic errors via intervals of estimated lengths. … the author proposes the generalized Gaussian approach presented here as one which produces reliable measurement uncertainties meeting the demands of traceability.” (Rainer Schlittgen, Zentralblatt MATH, Vol. 1210, 2011) From the Back Cover 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. About the Author 1967 Graduation in Physics at the Technical University of Stuttgart 1970 Doctorate at the Technical University of Braunschweig 1970 – 1975 Scientific assistant and lecturer at the Technical University of Braunschweig 1975 – 2004 Member of Staff at the Physikalische Technischer Bundesanstalt Braunschweig, commissioned to legal metrology, computerized interferometric measurment of length, measurement uncertainties and the adjustment of physical constants