Various metrics are not completely multiplicative, even though they are claimed to be. For example, mean alpha dispersion (0.3088132) and beta dispersion (0.1650757) do not sum to gamma dispersion (0.4725226) with the following data set (q=1, no abundances).
The issue is not likely to be related to whether or not one should always use the arithmetic mean (vs. a generalized mean dependent on p=1-q) to calculate Sw, M, and analogous components, because it should still be additive either way, in case q=0.
Various metrics are not completely multiplicative, even though they are claimed to be. For example, mean alpha dispersion (0.3088132) and beta dispersion (0.1650757) do not sum to gamma dispersion (0.4725226) with the following data set (q=1, no abundances).
FABdata.zip
The issue is not likely to be related to whether or not one should always use the arithmetic mean (vs. a generalized mean dependent on p=1-q) to calculate Sw, M, and analogous components, because it should still be additive either way, in case q=0.