  A new computational model for the description of the photon detector response
functions measured in conditions of low light is presented, together with
examples of the observed photomultiplier signal amplitude distributions,
successfully described using the parameterized model equation. In extension to
the previously known approximations, the new model describes the underlying
discrete statistical behavior of the photoelectron cascade multiplication
processes in photon detectors with complex non-uniform gain structure of the
first dynode. Important features of the model include the ability to represent
the true single-photoelectron spectra from different photomultipliers with a
variety of parameterized shapes, reflecting the variability in the design and
in the individual parameters of the detectors. The new software tool is
available for evaluation of the detectors' performance, response, and
efficiency parameters that may be used in various applications including the
ultra low background experiments such as the searches for Dark Matter and rare
decays, underground neutrino studies, optimizing operations of the Cherenkov
light detectors, help in the detector selection procedures, and in the
experiment simulations.
