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P. Filzmoser, K. Hron, A. Menafoglio:
"Logratio Approach to Distributional Modeling";
in: "Advances in Contemporary Statistics and Econometrics", A. Daouia, A. Ruiz-Gazen (ed.); Springer, Cham, 2021, ISBN: 978-3-030-73248-6, 451 - 470.

Distributional data, such as age distributions of populations, can be treated as continuous or discrete data, but the main interest is in the relative information, e.g., in terms of ratios (or logratios) between the different age classes. Here we present a unifying framework for the discrete and the continuous case based on the theory of Bayes spaces. While the discrete case is more widely treated in the literature, the continuous case allows to make a link to functional data analysis. Moreover, the methodological framework of Bayes spaces can also be used to develop methods for analyzing several distributional variables simultaneously. It turns out that the centered logratio transformation is a convenient tool for practical computations. Two real data examples illustrate the usefulness of this framework.

http://dx.doi.org/10.1007/978-3-030-73249-3_23

https://link.springer.com/chapter/10.1007/978-3-030-73249-3_23