<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we address measurement problems involving several quantities that are interrelated by model equations. Available knowledge about some of these quantities is represented by probability density functions (PDFs), which are then propagated through the model in order to obtain the PDFs attributed to the quantities for which nothing is initially known. A formalism for analyzing such models is presented. It comprises the concept of a „base parameterization“, which is used in conjunction with the change-of-variables theorem. The calculation procedure that results from this formalism is described in very general terms. Guidance is given on how to employ it in practice by presenting both an elementary example and a much more involved one.</p></abstract>

In this paper we address measurement problems involving several quantities that are interrelated by model equations. Available knowledge about some of these quantities is represented by probability density functions (PDFs), which are then propagated through the model in order to obtain the PDFs attributed to the quantities for which nothing is initially known. A formalism for analyzing such models is presented. It comprises the concept of a „base parameterization“, which is used in conjunction with the change-of-variables theorem. The calculation procedure that results from this formalism is described in very general terms. Guidance is given on how to employ it in practice by presenting both an elementary example and a much more involved one.

A Formalism for Expressing the Probability Density Functions of Interrelated Quantities

Department of Mechanical Engineering, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

Chemical Laboratories, Boehler Edelstahl, Mariazeller Str. 25, 8605 Kapfenberg, Austria

Measurement Science Review

In this paper we address measurement problems involving several quantities that are interrelated by model equations. Available knowledge about some of these...

A Formalism for Expressing the Probability Density Functions of Interrelated Quantities

Published Online: Apr 03, 2013

Page range: 50 - 55

DOI: https://doi.org/10.2478/msr-2013-0015

This content is open access.