Discrete mode-mixtures of unimodal positive distributions with an application to solar energy in South Africa
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Springer
Abstract
Comprehensive earth science studies consistently yield complex datasets seldom adequately represented by straightforward parametric distributions. In this paper, we introduce a discrete mode-mixture (DMM) model, motivated by the formulation of the mean mixture paradigm via the compounding method. Here, unimodal positive support mode-parameterized beta and gamma distributions represent the basic component, but with the superposition of a discrete random component on the mode. The probability density functions of the DMM models are derived in closed-form expressions, and specific characteristics are investigated. This alternative viewing of a mixture on the mode paves the way for alternative models and provides natural leverage on separation in data. With an emphasis on a solar dataset and a benchmark dataset, the performance of the proposed models is compared with that of well-known models.
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Keywords
Discrete mode-mixture (DMM), Beta, Compound, Gamma, Negative binomial, Poisson, SAURAN dataset
Sustainable Development Goals
SDG-07: Affordable and clean energy
SDG-13: Climate action
SDG-13: Climate action
Citation
Bekker, A., Otto, A.F., Punzo, A. et al. Discrete mode-mixtures of unimodal positive distributions with an application to solar energy in South Africa. Afrika Matematika 36, 115 (2025). https://doi.org/10.1007/s13370-025-01329-2.