Statistical Short-Cut Methods for the Rapid Location of Peak/Anomaly Positions in Two-Dimensional Crystallographic Data Histograms. Application of Order Statistics to Crystallographic Data Processing

Abstract

Statistical short-cut procedures involving the median, midrange and the mean are presented as methods for location of peak/anomaly positions in area-detector data. These methods test for normal distribution in uniform background intensities in which peak/anomaly magnitudes are considered as outlying data. Typically, the tests are applied to large data arrays where the background distributions are near normal with the statistic mean ≃ median ≃ [(x1:n + xn:n)1/2]. For data arrays with large intensity outliers, the statistic (x1:n + xn:n − 2 × median) and (mean − median) will be both greater than zero. If the outliers are censored, then ideally the above statistics will be equal to zero. Peak/anomaly pixel positions are identified as those pixels with magnitudes greater than the magnitude of the smallest censored point.