  It is generally known that counting statistics is not correctly described by
a Gaussian approximation. Nevertheless, in neutron scattering, it is common
practice to apply this approximation to the counting statistics; also at low
counting numbers. We show that the application of this approximation leads to
skewed results not only for low-count features, such as background level
estimation, but also for its estimation at double-digit count numbers. In
effect, this approximation is shown to be imprecise on all levels of count.
Instead, a Multinomial approach is introduced as well as a more standard
Poisson method, which we compare with the Gaussian case. These two methods
originate from a proper analysis of a multi-detector setup and a standard
triple axis instrument.We devise a simple mathematical procedure to produce
unbiased fits using the Multinomial distribution and demonstrate this method on
synthetic and actual inelastic scattering data. We find that the Multinomial
method provide almost unbiased results, and in some cases outperforms the
Poisson statistics. Although significantly biased, the Gaussian approach is in
general more robust in cases where the fitted model is not a true
representation of reality. For this reason, a proper data analysis toolbox for
low-count neutron scattering should therefore contain more than one model for
counting statistics.
