  The accurate calibration of photomultiplier tubes is critical in a wide
variety of applications for which it is necessary to know the absolute number
of detected photons or precisely determine the resolution of the signal.
Conventional calibration methods rely on fitting the photomultiplier response
to a low intensity light source with analytical approximations to the single
photoelectron distribution. We show that this approach often leads to biased
estimates due to an inability to model the full distribution accurately,
especially at low charge values. We present a simple statistical method to
extract the relevant single photoelectron calibration parameters (first two
central moments) without making any assumptions about the underlying single
photoelectron distribution. We illustrate the use of this method through the
calibration of a Hamamatsu R11410 photomultiplier tube and study the accuracy
and precision of the method using Monte Carlo simulations. The method is found
to have significantly reduced bias compared to conventional methods and works
under a wide range of light intensities, making it suitable for the
simultaneous calibration of large arrays of photomultiplier tubes where uniform
illumination may not be possible.
