Magister Scientiae - MSc (Statistics and Population Studies)

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Power studies of multivariate two-sample tests of comparison
(University of the Western Cape, 2007) Siluyele, Ian John; Koen, Chris
The multivariate two-sample tests provide a means to test the match between two multivariate distributions. Although many tests exist in the literature, relatively little is known about the relative power of these procedures. The studies reported in the thesis contrasts the effectiveness, in terms of power, of seven such tests with a Monte Carlo study. The relative power of the tests was investigated against location, scale, and correlation alternatives. Samples were drawn from bivariate exponential, normal and uniform populations. Results from the power studies show that there is no single test which is the most powerful in all situations. The use of particular test statistics is recommended for specific alternatives. A possible supplementary non-parametric graphical procedure, such as the Depth-Depth plot, can be recommended for diagnosing possible differences between the multivariate samples, if the null hypothesis is rejected. As an example of the utility of the procedures for real data, the multivariate two-sample tests were applied to photometric data of twenty galactic globular clusters. The results from the analyses support the recommendations associated with specific test statistics.
Female unemployment in South Africa: insight from the 2021 labour force survey.
(University of the Western Cape, 2023) Mfubu, Anele; Nsengiyumva, Philomene
The study focused on female unemployment and aimed to establish whether or not there is a relationship between female unemployment and demographic characteristics, whether the currently unemployed have ever worked or not, their duration of unemployment and the reasons for not working. It utilized the existing dataset from Statistics South Africa's fourth-quarter of 2021 Labour Force Survey. The study suggested that there are differentials in female unemployment, according to demographic characteristics. More precisely the greatest share percentage of unemployed females in South Africa was found within 25-34 age group and who are single. Nonetheless, those within 15-24 most of them were found among those who have never worked before, while a high percentage share of those who have work experience was found in 55-64 age group.
Assessing the high-risk behaviour of first year students entering the University of the Western Cape
(University of the Western Cape, 2007) Abels, Melissa Dione; Blignaut, R. J; Doctor, H. V
Globally, new HIV infections are heavily concentrated among the youth, i.e., persons aged 15-24 years old (UNAIDS, 2006b). In South Africa, the estimated national HIV prevalence was 10.4% among the youth in 2006 (Dorrington et a|.2006). The 2005-2006 national South African HIV rates ranged from 31.8o/oto39.3% among female youth and from 7.5oh to 10.1o/o among male youth (Dorrington et al. 2006; Pettifor et al. 2004; Shisana et al. 2005). UNAIDS (2006) stated that the future course of the HIV epidemic hinges on the high-risk behaviours the youth adept or maintain. The motivation for the study is to assess the high-risk behaviours that contribute to the spread of HIV and AIDS among the youth. The most influential high-risk behaviours that contribute to the spread of HIV and AIDS are unprotected sexual intercourse and having more than one sexual partner (Nattrass, 2004, Pettifor et al. 2004; Shisana et al. 2005; UYF & HSRC, 2005). Those who are in violent relationships, fear the threat of violence, which prevents them from insisting on condom use and this increases the risk of HIV infection (MacPhail & Campbell, 2001). Factors that leave the youth unable to set boundaries on when they want to have sex, what type of sex, or the use of contraception increase the risk of HIV infection. These factors include transactional sex, young age at first sex, cigarette smoking, alcohol use, drug use and suicidal behaviour (Aitken, 2005; Basile et al. 2006; Flisher et al. 1993c; Kauftnan & Stavrou, 2002; Pettifor et al. 2004; Shisana et aI.2005\. The population for this study included all full time first year students who registered at UWC for the first time in 2006 that attended the orientation week. A stratified, sequential random sample was drawn from the students attending the orientation. The Science Faculty Research Committee of UWC gave the consent to undertake the study. Informed consent was obtained from the 796 respondents and anonymity of their participation was ensured. The measuring instrument was a self-administered questionnaire. SAS package (SAS Institute Inc. 2004-2005) was used to clean the data and to do the analyses. Frequencies and percentages were provided for nominal and medians were provided for ratio scales. Rao-Scott Chi-square test was used to test the bivariate analysis between the high-risk behaviours. Multivariate logistic regression models were used to provide a clearer perspective on the effects of high-risk behaviours on non-condom use at last sex
A statistical investigation into the admissions criteria for the Electrical- and Mechanical Engineering courses at the Peninsula Technikon
(University of the Western Cape, 1995) Booysen, Desmond Reginald; Kotze, D.
Concern was expressed by the School of Electrical- and Mechanical Engineering and Computer Data Processing (School of EMC) regarding the School's admissions criteria for the Electrical- and Mechanical Engineering courses. Admission to these courses was primarily based on candidates' matric performance. The results of an aptitude test were used as a secondary criterion in selecting "academically risk" students. This investigation focused mainly on the following issues: The use of cut-off points in matric results and an aptitude test as admissions criteria. Identification of Matric subjects and/or aptitude test components that might assist in the selection of potentially successful of candidates. This study reports on Chaid and discriminant analyses performed to identify the important predictors of successful study. From the results of these tests regression models were constructed that were used to determine expected pass rates in first semester subjects. The Swedish rating was the best predictor of successful first semester study. An admissions Swedish score of at least 35 is recommended. The aptitude test total was found to be not significant in identifying potentially successful candidates. However, individual aptitude test components were significant in describing performance in specific first semester subjects.
Stigmatization of and discrimination against people who are HIV positive, or have AIDS - a female perspective in Zwartwater, Eastern Cape Province
(University of the Western Cape, 2011) Malgas, Khangela Frida; Blignaut, R.
The aim of this study is to investigate the perceived stigmatization of and discrimination against people who are HIV positive or people who are living with AIDS. One questionnaire was used to collect qualitative and quantitative data. Data collection was conducted for a period of three weeks in the Eastern Cape province at the Zwartwater area in Lady Frere and at the Queenstown (Frontier) Hospital. A sample of 170 (of the 900) females was interviewed, of which 100 were sequentially sampled from the community and 70 were sequentially sampled whilst they were queuing at the Queenstown (Frontier) Hospital for care. Households from the rural area were selected by visiting every fourth house on the route linking the houses in this area. At the hospital, selection started at the back of the queue and every sixth person was selected and interviewed. Scores were calculated for knowledge and attitudes towards people who are HIV positive and towards people who have AIDS. It was found that knowledge and attitude scores did not differ between the various age groups tested. It was furthermore found that an increased knowledge score improved attitudes towards people who are HIV-positive or have AIDS.
Modelling risk factors related to the performance of two oceans half marathon runners between 2012 and 2015
(University of the Western Cape, 2022) Jordaan, Marlise; Brydon, Humphrey
Limited literature is available on the effect of factors associated with the improvement in performance of Two Oceans Half Marathon (TOHM) runners. This study examined factors associated with the improvement in performance of a runner over a 4-year period for the Two Oceans Half Marathon through the application of a linear mixed model. A subset of data was identified that according to the literature had an impact on the performance of a half marathon runner. Univariate analysis was conducted to identify factors that had an impact on the performance of the runners and a linear mixed model was applied to the model adjusted for age, gender and body mass index (BMI) containing interaction effects to determine the extent to which these factors influence the change in performance of the runners.
Investigation of telecommunication recommender systems for curated post-paid products
(University of the Western Cape, 2023) Eachells, Brent Jesse; Steel, Sarel
Telecommunication recommender systems
Assessing the effect of imbalance correction through oversampling in the prediction of injury prevalence in distance runners
(University of the Western Cape, 2023) Ngoto, Simcengile; Luus, Retha
Prediction of injury prevalence in distance runners
A clustering smart phone users based on the digimiter survey and mobile application data
(University of the Western Cape, 2023) Kuse, Buhle; Brydon, Humphrey
Digimiter Survey
Religion, education and child immunization in Ethiopia
(University of the Western Cape, 2007) Lerebo, Wondwossen Terefe; Doctor, Henry Victor
This study examines the relationship between immunization status of children and religion before and after controlling for other factors such as maternal education in Ethiopia, a country characterized by highest mortality and morbidity rates in the world. Using data from the nationally representative 2000 Demographic and Health Survey, the bivariate results indicated that there are substantial differences in child immunization by maternal religion. More children born to traditional mothers are significantly less likely to receive full immunization coverage than children born to mothers professing Orthodox religion and other religions. The social mechanism that explains this huge disparity is that traditional mothers may be attributable to the traditional spiritual explanation of events, including diseases, and do not believe in the prevention of child-killer diseases. Further, significant variation in receiving complete immunization is observed with mother's level of education, and place of residence (rural/urban).
The AIDS transition: Impact of HIV/ AIDS on the demographic transition of black/ African South Africans by 2021
(University of Western Cape, 2004) Matanyaire, Sandra D.; Shell, R.C.-H.
The first two official AIDS cases were diagnosed in South Africa in 1982. During the same period of the 1980s, the black/ African population was experiencing an accelerated fertility decline, following a period of accelerated mortality decline. Demographers invoked the demographic transition theory to explain the observed mortality and fertility decline. According to the demographic transition theory, mortality and fertility rates would continue declining to low, post transitional levels with increasing modernization. The relatively higher prevalence of HIV/ AIDS estimated among black/ African South Africans is expected to alter their demographic transition. This research investigates the impact of HIV/ AIDS on the demographic transition of black/ Africans by 2021.
Estimation of Pareto Distribution Functions from Samples Contaminated by Measurement Errors
(University of the Western Cape, 2010) Kondlo, Lwando Orbet; Koen, Chris
Estimation of population distributions, from samples that are contaminated by measurement errors, is a common problem. This study considers the problem of estimating the population distribution of independent random variables Xi, from error-contaminated samples ~i (.j = 1, ... , n) such that Yi = Xi + f·.i, where E is the measurement error, which is assumed independent of X. The measurement error ( is also assumed to be normally distributed. Since the observed distribution function is a convolution of the error distribution with the true underlying distribution, estimation of the latter is often referred to as a deconvolution problem. A thorough study of the relevant deconvolution literature in statistics is reported. We also deal with the specific case when X is assumed to follow a truncated Pareto form. If observations are subject to Gaussian errors, then the observed Y is distributed as the convolution of the finite-support Pareto and Gaussian error distributions. The convolved probability density function (PDF) and cumulative distribution function (CDF) of the finite-support Pareto and Gaussian distributions are derived. The intention is to draw more specific connections bet.ween certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher's information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available. Simulated data are used to validate the methodology. A real-life application of the methodology is illustrated by fitting convolved distributions to astronomical data
Fitting extreme value distributions to the Zambezi River flood water levels recorded at Katima Mulilo in Namibia (1965-2003)
(University of the Western Cape, 2005) Kamwi, Innocent Silibelo; Koen, Chris; Blignaut, Renette J
This study sought to identify and fit the appropriate extreme value distribution to flood data, using the method of maximum likelihood. To examine the uncertainty of the estimated parameters and evaluate the goodness of fit of the model identified. The study revealed that the three parameter Weibull and the generalised extreme value (GEV) distributions fit the data very well. Standard errors for the estimated parameters were calculated from the empirical information matrix. An upper limit to the flood levels followed from the fitted distribution.
Development of a challenger price sensitivity model to improve Santam's new business optimisation framework
(University of the Western Cape, 2021) Engelke, Nina; Brydon, Humphrey
Site selection and community participation in the development of Gracilaria Gracilts (stackhouse) steentoft, irvine and farnham mariculture in the Western Cape province, South Africa.
(University of the Western Cape, 1999) Brown, Bernadette; Keats, Derek W.; Anderson, Robert J.
The seaweed Gracilaria gracilis has been shown in previous studies to have potential for mariculture along the West Coast of South Africa. However, the selection of suitable sites is crucial for the success of a farming enterprise. The variables important in the success or sustainability of suspended raft culture, and the environmental factors influencing these variables, were identified through a literature review. A suitable site was defined as a site with surface water temperature of between 10 and 17 "C, water depth of between 2 and 10 m below surface, and wave heights of less than 4 m. Data and information about these factors were obtained from sources such as the Sea Fisheries Research Institute, the SADCO database, the CSIR and from volunteers in St Helena Bay. The objectives of this study were to convert available data into formats that could be used in a Geographical Information System (GIS), and to predict suitable and available sites for suspended cultivation of Gracilaria gracilis in Saldanha Bay, Langebaan Lagoon and St. Helena Bay. Data were converted to digital format and data layers created. Each data layer represented suitable and unsuitable areas. Areas with existing mariculture, harbours, ship traffic zones and other uses were excluded to determine the real available areas. The Saldanha Bay-Langebaan lagoon system and St Helena Bay, have sites that show potential for suspended cultivation of G. eracilis. The total sizes of the areas selected as suitable are 975.4 ha in Saldanha Bay and 474.8 ha in St. Helena Bay. Some sites predicted as suitable are located in areas known to be subject to conditions not suitable for seaweed mariculture, and led to the conclusion that the accuracy of input data or method of analysis must be improved.
Evaluation of computer-based tutorials at UWC: Perceptions, advantages and challenges
(University of the Western Cape, 2003) Jonas, Sbongile; Kotze, D.
This is an exploratory study that aims to find out how computer-based tutorials can be conducted effectively for large first year Statistics classes. The study focuses on the student's perceptions, advantages of being able to access tutorials anywhere, anytime and lastly the challenges of implementing the system. More specifically for the University of the Western Cape (UWC) environment, without sufficient staff, the effectiveness of learning in this initial stage is focused on the experience whereby students can do extensive problem-solving anytime and anywhere. Data were collected at UWC using first-year introductory Statistics students, during the first and the second semester. Structured questionnaires (self-completed) were used to measure student's perceptions and learning experiences. The results pointed to a positive overall perception towards computers and feelings about computers amongst all groups of first year students. The major advantage with these randomly generated computer-based tutorials is the fact that one could access the questions anytime, anywhere. The challenge now remains with educators to provide an environment where new methods of learning and delivering information can be accessed effectively.
Minimising the Cost of Portfolio Guarantees by Controlling Volatility
(University of the Western Cape, 2021) Ehler, Jan; Kruger, Machiel
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Understanding the factors related to subjective well-being in the TB population: The South African perspective
(University of the Western Cape, 2020) Matatiele, Motladi; Stiegler, Nancy
Fifty percent of the world’s tuberculosis population is found in eight countries, one of which is South Africa. Of the eight countries, South Africa is said to be experiencing the highest burden of Tuberculosis, with an estimated incidence of three hundred and twenty-two thousand cases of active Tuberculosis. The Tuberculosis epidemic is driven by the following reasons, firstly poor living conditions which are a result of the wide gap between the rich and the poverty-stricken among some populations, and secondly late presentation to health facilities. Over the years, healthcare programs have made a meaningful impact in identifying patients presenting for Tuberculosis care, a global Tuberculosis report shows an estimated fifty-eight million lives were saved through Tuberculosis treatment and diagnosis, between the years 2000 and 2018. However, strategies to modify risk behaviour need to remain a main priority. In the South African context, it would be important to note the diversity of the individuals experience which is rooted in South African socio-political history and has resulted in high levels of social inequality and disparate socio-economic status groups, as a significant factor when considering the well-being of Tuberculosis infected South Africans. For policy makers to make data-driven decisions, with the aim of lessening the disease burden experienced by the populations they serve. They would require insights from an individual level, this way of measuring well-being requires the participants to rely on their own cognitive judgements and emotional reactions to characterize their well-being. Alatartseva and Barysheva in 2015 claim that subjective well-being is an internal evaluation of well-being, relating to one’s spiritual, personal characteristics and features. This approach is fitting since behavioural data is dynamic and relative as it tends to differ across populations and is often altered radically in short periods. Despite global advances in access to Tuberculosis treatment, Tuberculosis is the leading cause of death in adults with Human Immunodeficiency Virus and the main contributor to antimicrobial resistance. This gap can be bridged by an understanding of the behavioural aspects tied to Tuberculosis infection. There is a lack of adequate South African literature on Tuberculosis infection and health related well-being. The current study notes and compares, the diversity of life satisfaction experience between participants from different socio-demographic status groups across South Africa, bringing forth the most influential variables on well-being. This paper explored the possible factors of subjective well-being in the Tuberculosis infected South African population. Data from the National Income Dynamics Study 2017 was used, with a focus on the Tuberculosis diagnosed sub-population across all nine provinces in South Africa. The study sample consisted of forty-four individuals who were measured against the following variables: age; gender; population group; place of residence in 1994; labour market participation, education; health; emotional health and well-being and social cohesion. The study employed, Multiple Correspondence Analysis to identify significant variables associated with the well-being of Tuberculosis infected individuals. The results show that the participants of African lineage presented with the lowest level of subjective well-being, followed by the Coloured population which was more likely to have a smoking habit to further decrease their level of well-being. Gender was a significant contributor to well-being with female participants reporting an overall lower level of subjective well-being compared to their male counterpart. Furthermore, those co-infected with Tuberculosis and Human immunodeficiency Virus while poverty-stricken presented with the lowest possible level as they are likely to be depressed, have a weakened immune system and experiencing medication non-adherence.
Seisoensfluktuasies in Industriële produksie en die Aandelemark met spesiale verwysing na die Suid - Afrikaanse situasie
(University of the Western Cape, 1991) Cilliers, Frans Pieter; Smit, E. vd M
In 1976 Rozeff and Kinney found that seasonality exists in the monthly rates of return on the New York Stock Exchange with peak periods in January. By making use of this information and the fact that the rates of return lag real activity by one month, Chang en Pinegar (1986) indicated that rates of return unidirectionally predict future growth rates in industrial production for large companies. They also found that the seasonal growth rates in industrial production partially reflect the January seasonals in the rates of return for small companies. This is inconsistent with the efficient market hypothesis. Altough numerous studies in South Africa have been conducted on the efficiency of the Johannesburg Stock Exchange, no one has departed from the viewpoint of seasonality. The aim of this study is to investigate the efficiency of the Johannesburg stock Exchange with respect to seasonality in industrial production. It will be shown that there is no relationship between rates of return and real activity in the majority of sectors. The clothing sector is inefficient in the sense that real activity unidirectionally predicts rates of return three months in advance. At a six months lag period there are strong relationships, in both ways, between rates of return and real activity for this sector, that also implies inefficiency. Lastly it will be indicated that the November peaks on the Johannesburg stock Exchange do not coincide with the January peaks found overseas and that they do not lag real activity by one month. In the international research the attention was mainly focussed on the size of companies and stock price sensitivity to changes in industrial production while in this paper it focusses on different sectors.
An investigation into the methodologies of value-at -risk and a simulation process of a portfolio of financial instruments.
(University of the Western Cape, 2004) Ballam, Gamal Abdel Hussein; Kotze, Danelle
Financial companies such as investment and commercial banks as well as insurance companies, mutual and pension funds hold assets in the form of financial instruments in portfolios. Nowadays, financial instruments have proliferated so much that there are so many forms of them namely: derivatives, common stock, corporate and government bonds, foreign exchange and contracts. With so many financial instruments, companies can have very large and diversified portfolios for which they must quantify the risk. With high profile calamities that have rocked the financial world lately, the need for better risk management has never been so in demand as before. Value-at-Risk (VaR) is the latest addition in the investor's toolkit as far as measurements of risk is concerned. This new measure of risk complements well the existing risk measures that exist.Unfortunately, VaR is not unanimous and it has attracted a lot of critics over the years. This research thesis is threefold: to introduce the reader to the VaR concept; to discuss the different methods that exist to calculate VaR; and, finally, to simulate the VaR of a portfolio of government bonds. The first part of this research is to introduce the reader to the general idea of risk forms and its management, the role that the existing risk measures have played so far and the coming up of the new technique, which is VaR. The pros and cons that accompany a new technique are discussed as well as the history of VaR. The second part is about the different methods that exist to compute the VaR of a portfolio. Usually, VaR methodologies fall into three categories namely: Parametric; Historical; and Monte Carlo. In this research, the advantages and disadvantages of these three methods are discussed together with a step-wise method on how to proceed to calculate the VaR of a portfolio using any of the three methods. The practical side of this thesis deals about the VaR simulation of a portfolio of financial instruments. The chosen financial instruments are four South African government bonds with different characteristics. VaR for this particular portfolio will then be simulated by the three main methods. Eleven different simulations are run and they are compared against a Control Simulation (Benchmark Portfolio) to see how factors influencing VaR measure cope under different conditions. The main idea here was to check how VaR measures can change under different portfolio characteristics and to interpret these changes. Moreover, the VaR estimates under the three different methods will be compared

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