Compositional data

In statistics, compositional data are quantitative descriptions of the parts of some whole, conveying exclusively relative information.

This definition, given by John Aitchison (1986) has several consequences:

where D is the number of parts (components) and ${\displaystyle [\cdot ]}$ denotes a row vector.

This is the reason why ${\displaystyle \scriptstyle {\mathcal {S}}^{D}}$ is considered to be the sample space of compositional data. The positive constant ${\displaystyle \scriptstyle \kappa }$ is arbitrary. Frequent values for ${\displaystyle \scriptstyle \kappa }$ are 1 (per unit), 100 (percent, %), 1000, 10⁶ (ppm), 10⁹ (ppb), ...

...
Wikipedia