Fitting peaks with very low statistics

On a chi^2-function with previously estimated background

“…Suppose that during the experiment k data events are obtained and m background events were previously estimated using MC methods. Since the number of previously estimated MC events can depend on computational resources, it is possible to generate τ relative samples, such that τ = L MC /L EX P (1) where L EX P and L MC are the experimental and MC integrated luminosities, respectively, as said in high energy physics jargon. τ is the relative size of the MC background sample to the data sample and it is always larger than zero.…”

“…Non-Gaussian distributions are important, for example, in particle physics, where the experimental physicists have frequently to deal with counting experiment with few events data sets. A modified LSM was developed by Phillips [1] obtaining satisfactory results. Later Awaya [2] published an approach to fit data sets with poor statistic without the use of χ 2 -function minimization.…”

Multidimensional peak searching algorithm for low-statistics nuclear spectra

“…The basic classical peak searching algorithm based on SSD [2] and on the second derivative of the Gaussian used as the convolution function [11] can serve as good examples. In the peak searching procedure [12] it was claimed that for low-statistics the best result was achieved by the smoothing…”

The computer analysis of high resolution gamma-ray spectra from instrumental activation analysis experiments

“…As discussed by Phillips (1978), this may lead to biased results when fitting peaks with very low statistics, because those channels that have the fewest counts are given the greatest weight in the fitting process. Phillips has observed that the problem can be alleviated by using a three-point average or a five-point smoothing of the data to calculate the weights.…”