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Poisson errors and adaptive rebinning in X-ray powder diffraction data

This work provides a short summary of techniques for formally-correct handling of statistical uncertainties in Poisson-statistics dominated data, with emphasis on X-ray powder diffraction patterns. Correct assignment of uncertainties for low counts is documented. Further, we describe a technique for adaptively rebinning such data sets to provide more uniform statistics across a pattern with a wide range of count rates, from a few (or no) counts in a background bin to on-peak regions with many counts. This permits better plotting of data and analysis of a smaller number of points in a fitting package, without significant degradation of the information content of the data set. Examples of the effect of this on a diffraction data set are given.