  The accurate characterization of a photomultiplier tube (PMT) is crucial in a
wide-variety of applications. However, current methods do not give fully
accurate representations of the response of a PMT, especially at very low light
levels. In this work, we present a new and more realistic model of the response
of a PMT, called the cascade model, and use it to characterize two different
PMTs at various voltages and light levels. The cascade model is shown to
outperform the more common Gaussian model in almost all circumstances and to
agree well with a newly introduced model independent approach. The technical
and computational challenges of this model are also presented along with the
employed solution of developing a robust GPU-based analysis framework for this
and other non-analytical models.
