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A general algorithm for the decomposition of differences between two values of an aggregate demographic measure in respect to age and other dimensions is proposed. It assumes that the aggregate measure is computed from similar matrices of discrete demographic data for two populations under comparison. The algorithm estimates the effects of replacement for each elementary cell of one matrix by respective cell of another matrix. Application of the algorithm easily leads to the known formula fordoi:10.4054/demres.2002.7.14 fatcat:j4jcudcgfzhlrkk2lzctwnrrym