caa a22 4500 469064765 CHVBK 20180323132904.0 cr unu---uuuuu 170328e19920501xx s 000 0 eng 10.1007/BF00891269 doi (NATIONALLICENCE)springer-10.1007/BF00891269 Aitchison John Statistics Division, Department of Mathematics, Mathematics-Astronomy Building, University of Virginia, 22903, Charlottesville, Virginia aut On criteria for measures of compositional difference [Elektronische Daten] [John Aitchison] Simple perceptions about the nature of compositions lead through logical necessity to certain forms of analysis of compositional data. In this paper the consequences of essential requirements of scale, perturbation and permutation invariance, together with that of subcompositional dominance, are applied to the problem of characterizing change and measures of difference between two compositions. It will be shown that one strongly advocated scalar measure of difference fails these tests of logical necessity, and that one particular form of scalar measure of difference (the sum of the squares of all possible logratio differences in the components of the two compositions), although not unique, emerges as the simplest and most tractable satisfying the criteria. International Association for Mathematical Geology, 1992 scale invariance nationallicence permutation invariance nationallicence perturbation invariance nationallicence covariance structure nationallicence subcomposition nationallicence equivalence classes nationallicence groups nationallicence Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/4(1992-05-01), 365-379 0882-8121 24:4<365 1992 24 11004 https://doi.org/10.1007/BF00891269 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00891269 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Aitchison John Statistics Division, Department of Mathematics, Mathematics-Astronomy Building, University of Virginia, 22903, Charlottesville, Virginia aut NATIONALLICENCE 773 0- Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/4(1992-05-01), 365-379 0882-8121 24:4<365 1992 24 11004 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer