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Logratio Approach to Distributional Modeling

In: Advances in Contemporary Statistics and Econometrics

Author

Listed:
  • Peter Filzmoser

    (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics)

  • Karel Hron

    (Palacký University, Department of Mathematical Analysis and Applications of Mathematics)

  • Alessandra Menafoglio

    (Politecnico di Milano, MOX, Department of Mathematics)

Abstract

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.

Suggested Citation

  • Peter Filzmoser & Karel Hron & Alessandra Menafoglio, 2021. "Logratio Approach to Distributional Modeling," Springer Books, in: Abdelaati Daouia & Anne Ruiz-Gazen (ed.), Advances in Contemporary Statistics and Econometrics, pages 451-470, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73249-3_23
    DOI: 10.1007/978-3-030-73249-3_23
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