Publication
Parametric models for distributional data
| Summary: | 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. |
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| Main Authors: | Brito, Paula |
| Other Authors: | Silva, A. Pedro Duarte |
| Subject: | Analysis of variance Discriminant analysis Histogram data Symbolic data |
| Year: | 2025 |
| Country: | Portugal |
| Document type: | research article |
| Access type: | open access |
| Associated institution: | Universidade Católica Portuguesa |
| Language: | English |
| Origin: | Veritati - Repositório Institucional da Universidade Católica Portuguesa |
| Summary: | 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. |
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