@article{Egozcue_Pawlowsky-Glahn_2016, title={Changing the Reference Measure in the Simplex and its Weighting Effects}, volume={45}, url={https://www.ajs.or.at/index.php/ajs/article/view/vol45-4-2}, DOI={10.17713/ajs.v45i4.126}, abstractNote={<pre><!--StartFragment-->Standard analysis of compositional data under the assumption that the <span>Aitchison</span> geometry holds assumes a uniform distribution as reference measure of the space. Weighting of parts can be done changing the reference measure. The changes that appear in the algebraic-geometric structure of the simplex are analysed, as a step towards understanding the implications for elementary statistics of random compositions. Some of the standard tools in exploratory analysis of compositional data analysis, such as center, variation matrix and <span>biplots</span> are studied in some detail, although further research is still needed. The main conclusion is that down-weighting some parts is approaching the geometry of the corresponding <span>subcomposition</span>, thus preserving a kind of coherence between standard and down-weighted analyses.<!--EndFragment--></pre>}, number={4}, journal={Austrian Journal of Statistics}, author={Egozcue, Juan Jose and Pawlowsky-Glahn, Vera}, year={2016}, month={Jul.}, pages={25–44} }