  An analytical function is derived that exactly describes the amplification
process due to a series of discrete, Poisson-like amplifications like those in
a photo multiplier tube (PMT). A numerical recipe is provided that implements
this function as a computer program. It is shown how the program can be used as
the core-element of a faster, simplified routine to fit PMT spectra with high
efficiency. The functionality of the method is demonstrated by fitting both,
Monte Carlo generated and measured PMT spectra.
