Abstract

<h2>Acta Crystallographica</h2><h3></h3><h3>0365-110X</h3> <h2>research papers</h2> Volume 23 Part 6 Pages 888-898 December 1967 <h2>Statistical variance of line-profile parameters. Measures of intensity location and dispersion</h2> A. J. C. Wilson 888 Acta Cryst. (1967). 23, 888 Statistical Variance of Line-ProNe Parameters. Measures of Intensity, Location and Dispersion BY A. J. C. WILSON Physics Department, The University of Birmingham, P.O. Box 363, Birmingham 15, England (Received 13 March 1967) Diffractometric line profiles are ordinarily of little use in themselves, but are measured in order to derive from them some parameter of physical interest, such as the centroid position, the peak position, the variance, the integral breadth, the Fourier coefficients, etc. Since the counting rate Ij at the dif- fractometer setting 2~0~ is a random variable, all parameters derived from the Ij are also random variables, and in order to assess their reliability it is necessary to know their variances. Two methods of diffrac- tometer operation, fixed-time counting and fixed-count timing, are in common use, and a third, minimum- variance counting, has been suggested. Expressions for the variances of measures of intensity, location and dispersion are derived or quoted for all three methods of operation. Since for fixed-time counting the variances depend linearly