Multinomial, Poisson and Gaussian statistics in count data analysis

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