A new generalized class of distributions called the Burr-Weibull Power Series (BWPS) class of distributions is developed and explored. This class of distributions generalizes the Burr power series and Weibull power series classes of distributions, respectively. A special model of the BWPS class of distributions, the new Burr-Weibull Poisson (BWP) distribution is considered and some of its mathematical properties are obtained. The BWP distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential Poisson, Burr-exponential, Burr-Rayleigh Poisson, Burr-Rayleigh, Burr-Poisson, Burr, Lomax-exponential Poisson, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax-Poisson, Lomax, Weibull, Rayleigh and exponential distributions. Maximum likelihood estimation technique is used to estimate the model parameters followed by a Monte Carlo simulation study. Finally an application of the BWP model to a real data set is presented to illustrate the usefulness of the proposed class of distributions.

A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

The aim of the study was to determine the various needs facilitators and schools lack for effective teaching of science, technology, engineering, and mathematics (STEM) subjects, in both the primary and secondary under-resourced rural schools. This survey was conducted from February 2019 to March 2019, in Lupane and Hwange Districts. A multi-stage sampling method was used for collecting data. Focus group discussions were also used in collecting data and were conducted prior to issuance of questionnaires for completion by the participants. In analyzing data, odds ratio (OR) were calculated to compare the relative odds between outcomes and variables of interest. The survey found out that female facilitators were lagging behind in the uptake and training of teaching of STEM subjects, which could be attributed to family responsibilities. It was established that some needs such as lesson delivery skills, research skills and capacitation were highly needed in primary schools as compared to secondary schools. While other needs identified were equally needed in both primary and secondary schools. These include but are not limited to conducting team teaching with other facilitators, linking topics and lessons across classes and lessons, application skills and STEM activities. It was highly recommended that primary and secondary school facilitators be funded to attend capacitation platforms in teaching of STEM subjects for effective teaching of STEM in rural schools and using locally available resources, as limited resources is the order of the day in rural schools. Schools must be equipped with tools and structures such as laboratories. If schools cannot build laboratories, it was recommended that mobile laboratories be established to improve teaching of STEM subjects in under-resourced rural schools. One mobile laboratory can service many schools in the district and improve the pass rate of STEM subjects.

The renewable energy industry requires accurate forecasts of intermittent solar irradiance (SI) to effectively manage solar power generation and supply. Introducing the random forests (RFs) model and its hybridisation with quantile regression modelling, the quantile regression random forest (QRRF), can help improve the forecasts’ accuracy. This paper assesses the RFs and QRRF models against the quantile generalised additive model (QGAM) by evaluating their forecast performances. A simulation study of multivariate data-generating processes was carried out to compare the forecasting accuracy of the models when predicting global horizontal solar irradiance. The QRRF and QGAM are completely new forecasting frameworks for SI studies, to the best of our knowledge. Simulation results suggested that the introduced QRRF compared well with the QGAM when predicting the forecast distribution. However, the evaluations of the pinball loss scores and mean absolute scaled errors demonstrated a clear superiority of the QGAM. Similar results were obtained in an application to real-life data. Therefore, we recommend that the QGAM be preferred ahead of decision tree-based models when predicting solar irradiance. However, the QRRF model can be used alternatively to predict the forecast distribution. Both the QGAM and QRRF modelling frameworks went beyond representing forecast uncertainty of SI as probability distributions around a prediction interval to give complete information through the estimation of quantiles. Most SI studies conducted are residual and/or non-parametric modelling that are limited to represent information about the conditional mean distribution. Extensions of the QRRF and QGAM frameworks can be made to model other renewable sources of energy that have meteorological characteristics similar to solar irradiance.

Exploration of solar irradiance can greatly assist in understanding how renewable energy can be better harnessed. It helps in establishing the solar irradiance climate in a particular region for effective and efficient harvesting of solar energy. Understanding the climate provides planners, designers and investors in the solar power generation sector with critical information. However, a detailed exploration of these climatic characteristics has not yet been studied for the Southern African data. Very little exploration is being done through the use of measures of centrality only. These descriptive statistics may be misleading. As a result, we overcome limitations in the currently used deterministic models through the application of distributional modelling through quantile functions. Deterministic and stochastic elements in the data were combined and analysed simultaneously when fitting quantile distributional function models. The fitted models were then used to find population means as explorative parameters that consist of both deterministic and stochastic properties of the data. The application of QFs has been shown to be a practical tool and gives more information than approaches that focus separately on either measures of central tendency or empirical distributions. Seasonal effects were detected in the data from the whole region and can be attributed to the cyclical behaviour exhibited. Daily maximum solar irradiation is taking place within two hours of midday and monthly accumulates in summer months. Windhoek is receiving the best daily total mean, while the maximum monthly accumulated total mean is taking place in Durban. Developing separate solar irradiation models for summer and winter is highly recommended. Though robust and rigorous, quantile distributional function modelling enables exploration and understanding of all components of the behaviour of the data being studied. Therefore, a starting base for understanding Southern Africa’s solar climate was developed in this study.