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<p>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.</p>

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Discrete mode-mixtures of unimodal positive distributions with an application to solar energy in South Africa

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月4日

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  • A. Bekker,
  • A. F. Otto,
  • A. Punzo,
  • S. D. Tomarchio,
  • J. T. Ferreira

摘要

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.