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It is generally known that counting statistics is not correctly described bya Gaussian approximation. Nevertheless, in neutron scattering, it is commonpractice to apply this approximation to the counting statistics; also at lowcounting numbers. We show that the application of this approximation leads toskewed results not only for low-count features, such as background levelestimation, but also for its estimation at double-digit count numbers. Ineffect, this approximation is shown to be imprecise on all levels of count.Instead, a Multinomial approach is introduced as well as a more standardPoisson method, which we compare with the Gaussian case. These two methodsoriginate from a proper analysis of a multi-detector setup and a standardtriple axis instrument.We devise a simple mathematical procedure to produceunbiased fits using the Multinomial distribution and demonstrate this method onsynthetic and actual inelastic scattering data. We find that the Multinomialmethod provide almost unbiased results, and in some cases outperforms thePoisson statistics. Although significantly biased, the Gaussian approach is ingeneral more robust in cases where the fitted model is not a truerepresentation of reality. For this reason, a proper data analysis toolbox forlow-count neutron scattering should therefore contain more than one model forcounting statistics.

Multinomial, Poisson and Gaussian statistics in count data analysis