Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood Heights Time Series Models in the Lower Limpopo River Basin of Mozambique

In this paper we fit a generalised extreme value (GEV) distribution to annual maxima flood heights time series models: annual daily maxima (AM1), annual maxima of 2 days (AM2), annual maxima of 5 days (AM5) and annual maxima of 10 days (AM10). The study is aimed at identifying suitable annual maxima moving sums that can be used to best model extreme flood heights in the lower Limpopo River basin of Mozambique, and hence construct flood frequency tables. The study established that models AM5 and AM10 were suitable annual maxima time series models for Chokwe and Sicacate, respectively. This study also revealed that the year 2000 flood height was a very rare extreme event. Flood frequency tables were constructed for the two sites Chokwe and Sicacate in the lower Limpopo River basin of Mozambique and these tables can be used to predict the return periods and their corresponding return levels at the sites and their neighbourhood. It is our hope that these long term forecasts will complement the short term flood forecasting and early warning systems in the basin in reducing the associated risk and mitigating the deleterious impacts of these floods on humans and property

An evaluation of variable selection methods using Southern Africa solar irradiation data

Dimensionality poses a challenge in developing quality predictive models. Often when modelling solar irradiance (SI), many covariates are considered. Training such data has several disadvantages. This study sought to identify the best variable embedded selection method for different location and time horizon combinations from Southern Africa solar irradiance data. It introduced new variable selection methods into solar irradiation studies, namely penalised quantile regression (PQR), regularised random forests (RRF), and quantile regression forest (QRF). Stability analysis, performance and accuracy metric evaluations were used to compare them with the common lasso, elastic and ridge regression methods. The QRF model performed best in all locations followed by the shrinkage methods on hourly data. However, it was found that QRF is not sensitive to associations through correlations, thereby ignoring the relevance of variables while focusing on importance. Among the shrinkage methods, the lasso performed best in only one location. On the 24-hour horizon, elastic net dominated the performances among the shrinkage methods, but QRF was best in three locations of the six considered. Results confirmed that variable selection methods performed differently on different situational data sets. Depending on the strengths of the methods, results were combined to identify the most paramount variables. Day, total rainfall, and wind direction were superfluous features in all situations. The study concluded that shrinkage methods are best in cases of extreme multicollinearity, while QRF is best on data sets with outliers or/and heavy tails

Application of the Equipment Replacement Dynamic Programming Model in Conveyor Belt Replacement: Case Study of a Gold Mining Company

As assets age, they generally deteriorate, resulting in rising operating and maintenance costs and decreasing salvage values. In this paper a comprehensive Dynamic Programming-based optimisation solution methodology is used to solve the equipment replacement optimisation problem on the replacement of conveyor belts at a Gold Mining company in Zimbabwe. Given a mining setup with one and two-year old conveyor belts the ultimate objective is to keep or replace the conveyor belt such that the overall cost of material handling is minimised within a five-year period. The findings reveal that this mining system should replace conveyor belts yearly. It is concluded that, an equipment replacement policy for conveyor belts is a necessity in a mining system so as to achieve an optimal contribution to the economic value that a mining system may accrue within a period of time. DOI: 10.5901/mjss.2015.v6n2s1p60

Prevalence and predictors of illicit drug use among school-going adolescents in Harare, Zimbabwe

Objective: To estimate the prevalence and predictors of illicit drug use among school-going adolescents in Harare, Zimbabwe. Methods: We used data from the Global School-based Health Survey (GSHS) conducted in 2003 in Harare to obtain frequencies of a selected list of characteristics. We also carried out logistic regression to assess the association between illicit drug use and explanatory variables. For the purpose of this study, illicit drug use was defined as marijuana or glue use. Results: A total of 1984 adolescents participated in the study. Most of the sample were females (50.7%), 15-year- olds (30.3%), nonsmokers and non-alcohol drinkers. Nine percent of the subjects (13.4% males and 4.9% females) reported having ever used marijuana or glue. Males were more likely to have used marijuana or glue than females (OR=2.70; 95% CI [1.47, 4.96]). Marijuana or glue use was positively associated with cigarette smoking (OR=11.17; 95% CI [4.29, 29.08]), alcohol drinking (OR=7.00; 95% CI [3.39, 14.47]) and sexual intercourse (OR=5.17; 95% CI [2.59, 10.29]). Parental supervision was a protective factor for marijuana or glue use (OR=0.31; 95% CI [0.16, 0.61]). Conclusions: Public health intervention aimed to prevent marijuana or glue use among adolescents should be designed with the understanding that illicit drug use may be associated with other behaviors such as teenage sexual activity, cigarette smoking and alcohol use

Relating Glycemia Levels in a Zimbabwean Population to some established Type 2 Diabetes Risk Factors using Multiple LinearRegression Analysis

Chronic non-communicable diseases such as diabetes and asthma are somewhat neglected in the field of medicine in favour of the more ?classic? infections such as HIV/AIDS,and tuberculosis. The overall worldwide prevalence of diabetes is gradually increasing and is mainly associated with many chronic vascular complications such as stroke, foot ulceration and coronary artery disease. For this reason a multiple linear regression model is proposed that will provide insights into the major risk factors of Type 2 diabetes. Objectives: The objective of this study is to examine the relationship between glycemia and some established Type 2 diabetes risk factors; in particular, stress, age, obesity, gender, and hypertension using multiple linear regression in the Zimbabwean population. Methods: The method consists of collecting data using a structured questionnaire from a sample of 300 individuals selected from a population through the ?haphazard? sampling technique. In this study we considered Type 2 diabetes because our assessment of glycemia was based on portable glucometer readings. We then develop a statistical model to predict glucose levels. Results: Two predictor variables age and body mass index were found to be significant in the model. Results show an overwhelming evidence of a strong relationship between age, obesity and Type 2 diabetes. Conclusion: Our findings are in agreement with results from Sudan in Africa and also observations from affluentsocieties. However, these findings differ significantly from other African experiences such as Kenya. Without loss of generality, it is concluded that obesity and advancing age are major contributors of Type 2 diabetes

Comparative Analysis of the 100-Year Return Level of the Average Monthly Rainfall for South Africa: Parent Distribution versus Extreme Value Distributions

In this paper, we model average monthly rainfall for South Africa using the parent distribution and extreme value theory (EVT). The 100-year return level plays an important role to hydrologists, meteorologists and civil engineers. Hence, the paper focuses on modelling the 100-year return level of average monthly rainfall for South Africa using the parent distribution and EVT. The present paper aims to compare the extreme quantile estimates of the EVT and parent distributions as well as to reveal the risk brought by heavy rainfall in South Africa. The method of maximum likelihood was used to estimate unknown parameters. We first investigate the parent distribution of the average monthly rainfall for South Africa. The results showed that the two-parameter Weibull distribution, which is in the domain of attraction of the Weibull family, is the appropriate parent distribution to model the data. We then perform a comparative analysis of the 100-year return level using the two-parameter Weibull distribution, the generalised extreme value distribution (GEVD), and the Poisson point process. The findings revealed that the 100-year return level of the two-parameter Weibull distribution was lower compared to that of the GEVD and Poisson point process model. The 100-year return level of the GEVD was equal to that of the observed maximum for the series, whereas that of the Poisson point process was slightly higher than the observed maximum average monthly rainfall for South Africa. Moreover, EVT models gave higher quantile estimation of the 100-year average monthly rainfall for South Africa compared to the parent distribution. Furthermore, EVT based estimation gave narrower confidence intervals as compared to the wider confidence interval of the parent distribution. Therefore, EVT models can play an important role in disaster risk reduction and civil engineering constructions, such as bridges and dams

An Investigation of Risk Factors Associated with Tuberculosis Transmission in South Africa Using Logistic Regression Model

Background: South Africa has a high burden of tuberculosis (TB) disease and is currently not meeting the national and international reduction outcome targets. The TB prevalence rate of South Africa in 2015 was estimated at approximately 690 per 100,000 population per year, with an incidence rate of about 834 per 100,000 population. This study examines risk factors associated with development of TB in South Africa. Materials and Methods: This study utilised readily available open access secondary data of 2019 South African Health and Demographic Survey from Statistics South Africa (StatsSA) website, which was collected from self-reported information relating to TB in the household questionnaire. The factors analysed were of demographic, socio-economic and health nature. Bivariate and binary logistics analyses were carried out from which appropriate inferences were drawn on the association of TB with demographic, socio-economic and health factors. Results: In multivariate analysis the study revealed that age, personal weight, smoke, alcohol, asthma, province of residence, race and usually coughing were significantly associated with an increased risk of having TB. Conclusions and Recommendations: The results strongly suggest that young and older people coming from black and coloured ethic groups, who are asthmatic and cough frequently, and/or smoking and consuming alcohol are at high risk of developing TB. In addition, those who are overweight appear to have an increased risk of TB transmission, with the Western Cape, Eastern Cape, Northern Cape, Free State, North West and Gauteng being the hardest hit provinces. Hence, the study recommends that these factors must be taken into account in the planning and development of TB policies in order to work successfully towards the achievement of sustainable development goal of reducing TB by 80% before 2030

An Investigation of Parent Distributions and Long-Term Trends of Average Maximum and Minimum Temperature in the Limpopo Province of South Africa

In studying natural hazards or disasters that occur due to temperature extremes such as heat waves and cold waves, it is crucial to understand the underlying distributions of the maximum and minimum temperatures at a particular site or region. The present study intends to investigate the parent distributions of maximum and minimum temperatures at various sites in the Limpopo province of South Africa. The parent distributions were investigated at four meteorological stations in Limpopo province, namely: Mara (1949-2018), Messina (1934-2009), Polokwane (1932-2018) and Thabazimbi (1994-2018). Four candidate parent distributions; normal, lognormal, gamma and Weibull distributions, were fitted to the average monthly maximum and minimum daily temperatures. Prior to the selection of the parent distributions, the data set at each station was subjected to normality test using the Shapiro-Wilk (SW) and Jarque-Bera (JB) tests. The normality tests have revealed that the maximum and minimum temperature data series at all the stations do not follow a normal distribution. Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to select the best fitting distribution at a particular site. The parent distribution with the lowest value of AIC and BIC was chosen as the best fitting distribution for the data. Goodness-of-fit diagnostic tests such as the Q-Q plots, P-P plots, empirical and theoretical density and cumulative distribution function (CDF) plots were conducted on the selected and/or competing candidate distributions. The findings reveal that short-tailed distributions in the Weibull domain of attraction, which include the Weibull distribution, are the best fitting parent distributions for both maximum and minimum temperature series at all the stations. Furthermore, a generalised extreme value (GEV) distribution was fitted to all the data set for each station in order to establish and validate whether the Weibull family is indeed a good fit to the data. The GEV distribution findings further confirmed the Weibull class as the parent distribution for all the stations in the study. The Mann-Kendall test and time series plots trend analysis findings have shown that there is a downward and upward long-term trend in minimum and maximum temperature data, respectively. Future studies will look into the possibility of applying both univariate and multivariate extreme value theory (MEVT) techniques to investigate further whether these climatic changes in mean monthly temperature can indeed be attributed to global warming and other natural modes of interdecadal variabilit

Modelling Long-Term Monthly Rainfall Variability in Selected Provinces of South Africa: Trend and Extreme Value Analysis Approaches

Extreme rainfall events have made significant damages to properties, public infrastructure and agriculture in some provinces of South Africa notably in KwaZulu-Natal and Gauteng among others. The general global increase in the frequency and intensity of extreme precipitation events in recent years is raising a concern that human activities might be heavily disturbed. This study attempts to model long-term monthly rainfall variability in the selected provinces of South Africa using various statistical techniques. The study investigates the normality and stationarity of the underlying distribution of the whole body of rainfall data for each selected province, the long-term trends of the rainfall data and the extreme value distributions which model the tails of the rainfall distribution data. These approaches were meant to help achieve the broader purpose of this study of investigating the long-term rainfall trends, stationarity of the rainfall distributions and extreme value distributions of monthly rainfall records in the selected provinces of South Africa in this era of climate change. The five provinces considered in this study are Eastern Cape, Gauteng, KwaZulu-Natal, Limpopo and Mpumalanga. The findings revealed that the long-term rainfall distribution for all the selected provinces does not come from a normal distribution. Furthermore, the monthly rainfall data distribution for the majority of the provinces is not stationary. The paper discusses the modelling of monthly rainfall extremes using the non-stationary generalised extreme value distribution (GEVD) which falls under the block maxima extreme value theory (EVT) approach. The maximum likelihood estimation method was used to obtain the estimates of the parameters. The stationary GEVD was found as the best distribution model for Eastern Cape, Gauteng, and KwaZulu-Natal provinces. Furthermore, model fitting supported non-stationary GEVD model for maximum monthly rainfall with nonlinear quadratic trend in the location parameter and a linear trend in the scale parameter for Limpopo, while in Mpumalanga the non-stationary GEVD model with a nonlinear quadratic trend in the scale parameter and no variation in the location parameter fitted well to the monthly rainfall data. The negative values of the shape parameters for Eastern Cape and Mpumalanga suggest that the data follow the Weibull distribution class, while the positive values of the shape parameters for Gauteng, KwaZulu-Natal and Limpopo suggest that the data follow the Fréchet distribution class. The findings from this paper could give information that can assist decision makers establish strategies for proper planning of agriculture, infrastructure, drainage system and other water resource applications in the South African provinces