Parametric models for distributional data

Paula Brito () and A. Pedro Duarte Silva ()
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Paula Brito: Universidade do Porto, Faculdade de Economia
A. Pedro Duarte Silva: Universidade Católica Portuguesa, Católica Porto Business School and CEGE

Advances in Data Analysis and Classification, 2025, vol. 19, issue 4, No 10, 1119-1146

Abstract: Abstract We present parametric probabilistic models for numerical distributional variables. The proposed models are based on the representation of each distribution by a location measure and inter-quantile ranges, for given quantiles, thereby characterizing the underlying empirical distributions in a flexible way. Multivariate Normal distributions are assumed for the whole set of indicators, considering alternative structures of the variance–covariance matrix. For all cases, maximum likelihood estimators of the corresponding parameters are derived. This modelling allows for hypothesis testing and multivariate parametric analysis. The proposed framework is applied to Analysis of Variance and parametric Discriminant Analysis of distributional data. A simulation study examines the performance of the proposed models in classification problems under different data conditions. Applications to Internet traffic data and Portuguese official data illustrate the relevance of the proposed approach.

Keywords: Analysis of variance; Discriminant analysis; Histogram data; Symbolic data; 62R07; 62H30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11634-025-00624-x

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