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

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.