Using Burgess's variance theorem, it is shown that at binomial transitional characteristics, variances of photons and photoelectrons have identical functional form when photons have negative-binomial or Poisson distribution function. By direct calculation it is obtained that in this cases photoelectrons distribution function reproduces that of photons that is photoelectrons distribution function has negative-binomial or Poisson form.
Pavel S. Serebrennikov,
"Photoelectron statistics", Proc. SPIE 3819, International Conference on Photoelectronics and Night Vision Devices, (10 June 1999); doi: 10.1117/12.350895; https://doi.org/10.1117/12.350895