Department of Statistics & Population Studies

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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.
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.
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.
The AIDS transition: impact of HIV/AIDS on the demographic transition of black/African South Africans by 2021
(University of the Western Cape, 2004) Matanyaire, Sandra D.; Shell, Robert C.H.; Haldenwang, B.B.; Dept. of Statistics; Faculty of Science
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 investigated the impact of HIV/AIDS on the demographic transition of black/Africans by 2021.
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
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.
Placing the dead: the spatial distribution and spread of HIV in a major South African city
(University of the Western Cape, 2005) Rama, Parbavati; Shell, Robert C.H.; Dept. of Mathematics; Faculty of Science
The aim of this study was to establish a new understanding of the epidemiology of HIV/AIDS at the municipal level, but at the same time upholding the anonymity of the HIV infected and AIDS sufferers. Innovative research techniques such as the use of GIS (geographic information systems) as a research tool contributed to disclosing the patterns of the HIV pandemic in the Nelson Mandela Metropole that were not obvious or visible before. GIS involved geographic maps that detect the spatial relationship between HIV prevalence rates and vectors that drive the pandemic.
Fitting extreme value distributions to the Zambezi river flood water levels recorded at Katima Mulilo in Namibia
(University of the Western Cape, 2005) Kamwi, Innocent Silibelo; Koen, C; Blignaut, Renette; Dept. of Statistics; Faculty of Science
The aim of this research project was to estimate parameters for the distribution of annual maximum flood levels for the Zambezi River at Katima Mulilo. The estimation of parameters was done by using the maximum likelihood method. The study aimed to explore data of the Zambezi's annual maximum flood heights at Katima Mulilo by means of fitting the Gumbel, Weibull and the generalized extreme value distributions and evaluated their goodness of fit.
Quantified assessment to enhance student learning in the sciences at UWC
(University of the Western Cape, 2005) Lombard, Ronell; Blignaut, Renette; Dept. of Biotechnology; Faculty of Science
This project discusses whether the British prototype questionnaire called the Assessment Experience Questionnaire (AEQ) could be standardized as a quantifier of assessment and be used at a multicultural institute such as the University of the Western Cape (UWC). This questionnaire was created in the United Kingdom to assist lecturers in evaluating and developing their assessment systems.
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.
Throughput of UWC students who did at least one semester of third-year statistics
(University of the Western Cape, 2005) Latief, Abduraghiem; Blignaut, Renette; Kotze, D; Dept. of Statistics; Faculty of Science
This study explored the completion rates (the number of years a student takes to complete a degree) of graduates at the University of the Western Cape. Differences between students who finished their studies in the prescribed time of three years and those who took longer than the prescribed time was highlighted.
An application of factor analysis on a 24-item scale on the attitudes towards AIDS precautions using Pearson, Spearman and Polychoric correlation matrices
(University of the Western Cape, 2006) Abdalmajid, Mohammed Babekir Elmalik; Blignaut, Renette; Dept. of Statistics; Faculty of Science
The 24-item scale has been used extensively to assess the attitudes towards AIDS precautions. This study investigated the usefulness and validity of the instrument in a South African setting, fourteen years after the development of the instrument. If a new structure could be found statistically, the HIV/AIDS prevention strategies could be more effective in aiding campaigns to change attitudes and sexual behaviour.
Fertility in Rwanda: Impact of genocide, an ananlysis of fertility before, during and after 1994 genocide
(University of the Western Cape, 2006) Basuayi, Clement Bula; Stiegler, Nancy
The 20th century has witnessed several wars and genocides worldwide. Notable examples include the Armenian and Jews genocides which took place during World War I and World War II respectively. The Rwandan genocide of 1994 is a more recent example. These wars and genocides have impacted on the socio-economic and demographic transition with resounding crisis. The present study focused on the Rwandan genocide which affected households and families by reducing the fertility rate. Hence the fertility transition in Rwanda was analyzed for the period before, during and after genocide.
Investigating domestic violence against women in South Africa
(University of the Western Cape, 2006) Njezula, Aurelia Babalwa; Stiegler, Nancy; Dept. of Statistics; Faculty of Science
Domestic violence or intimate partner violence is increasingly being recognized as a problem that seems to be spiralling out of control. The causes of domestic violence have preoccupied scientists for several decades. The hypothesis that domestic violence might be biologically determined was significantly undermined by observations that its occurrence varies considerably between, as well as within, societies. The aim of this study was to add to the growing, but still rather fragmented, body of knowledge in South Africa on violence against women. This study seeks to analyze domestic violence from an angle whereby the data can be explored to find factors contributing to women experiencing domestic violence in South Africa. The objectives of this research are to measure the prevalence of physical, sexual and financial abuse and to identify a profile of women who have experienced domestic violence.
Perceived quality and utilisation of maternal health services in peri-urban, commercial farming, and rural areas in South Africa
(University of the Western Cape, 2006) Matizirofa, Lyness; Jackson, D; Blignaut, Renette; Dept. of Statistics; Faculty of Science
This investigation aimed to determine factors that influence women's utilisation of maternal health services, with specific focus on the quality of care and services available to disadvantaged communities in South Africa. It used the women's perspectives to assess the quality of maternal healthcare services in peri-urban commercial farming and rural areas with the purpose of understanding why women utilise maternal services the way they do.
Waiting to die: staging of HIV positive people at the first HIV test - Region A, Nelson Mandela Metropole (January 1991-April 2000)
(University of the Western Cape, 2006) Cupido, Ynoma; Stiegler, Nancy; Blignaut, Renette; Dept. of Statistics; Faculty of Science
This project suggested that HIV people in Region A (Nelson Mandela Metropole, formerly Port Elizabeth) health district of the Eastern Cape, seek HIV testing when they are already in stages three (late disease) and four (AIDS) of HIV infection. Data had been obtained from the AIDS Training Information and Counselling Centre in the Nelson Mandela Metropole in 2000. The consequences of diagnoses only in the advanced stages of HIV infection will have a devastating impact on case management. Therefore, this paper yielded important data for South African policy makers to write health and welfare policies that might improve the quality of life of those terminally infected with HIV.
Location-based estimation of the autoregressive coefficient in ARX(1) models
(University of the Western Cape, 2006) Kamanu, Timothy Kevin Kuria; Koen, Chris; Dept. of Statistics; Faculty of Science
In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as ‘mean-unbiased’ and ‘medianunbiased’ estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1). However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the ‘medianunbiased’ estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed; the ‘most-probably-unbiased’ estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed; (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model; (3) the exact variance and MSE of LS estimator is determined; (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort; (5) an exact method of evaluating the density of the three estimators is described; (6) their exact bias, mean, variance and MSE are determined and analysed; and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed. The discussion and results show that the estimators are still biased in the usual sense: ‘in expectation’. However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation.
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).
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.

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