The statistics of multi-photoelectron pulse-height distributions

Multi-photoelectron pulse-height distributions feature in the scientific literature on light detectors, and yet there appears to have been no attempt to describe the statistics of such spectra. Formulas for pdfs are derived, assuming Poisson statistics, but more importantly for single-electron response curves of any description—analytical or experimental. The pdf generated by a pulsed light source, detected by a PMT of high d1 gain, agrees with statistical predictions.