  Transient responses in disordered systems typically show a heavy-tail
relaxation behavior: the decay time constant increases as time increases,
revealing a spectral distribution of time constants. The asymptotic value of
such transients is notoriously difficult to experimentally measure due to the
increasing decay time-scale. However, if the heavy-tail transient is plotted
versus log-time, a reduced set of data around the inflection point of such a
plot is sufficient for an accurate fit. From a derivative plot in log-time, the
peak height, position, line width, and, most importantly, skewness are all that
is needed to accurately predict the asymptotic value of various heavy-tail
decay models to within less than a percent. This curve fitting strategy reduces
by orders of magnitude the amount of experimental data required, and clearly
identifies a threshold below which the amount of data is insufficient to
distinguish various models. The skew normal spectral fit and dispersive
diffusion transient fit are proposed as four-parameter fits, with the latter
including the stretched exponential as a limiting case. The line fit and
asymptotic prediction are demonstrated using experimental transient responses
in previously published amorphous silicon and amorphous InGaZnO data.
