Bounded error analysis of experimental distributions of relaxation times

A method is presented for analyzing experimental data from dielectric relaxation, acoustic relaxation, or other measurements related to a distribution of relaxation times. A consistency test is derived showing whether or not there is any distribution of relaxation times consistent with the data. For consistent data, the analysis then provides bounds on possible interpolations at frequencies between the measured points. Bounds are placed on the cumulative distribution of relaxation times and these bounds are shown to be the most precise attainable on the basis of any given set of experimental data. The analysis is illustrated by application to ’’data’’ generated theoretically from some simple distributions of relaxation times and to some experimental data on dielectric relaxation.