Cumulants and moments in the line profile analysis

摘要

An analogy between diffraction profiles and probability distributions of random variables is a basis for the utilization of the mathematical formalism of the theory of probability in the line profile analysis. Namely, the first and the second moments were used to the describing of a position and a breadth of diffraction profiles. Higher moments were introduced also in the line profile analysis, especially the fourth moments for the estimation of the particle size and the microstrain from a single line. However, the formulas for these higher moments are more complicated. Besides the moments, cumulants of random variables were introduced in the theory of probability. The purpose of the contribution is to show, that the cumulants can be used very advantageously in the line profile analysis, especially instead of the higher moments of the diffraction profiles and in the case when number of convoluted functions is a higher as two.