Mathematical Statistics and Actuarial Science

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Open Access
The capability approach and measurement: operationalizing capability indicators in higher education
(University of the Free State, 2015-01) Ruswa, Anesu; Walker, Melanie; Chikobvu, Delson
The thesis contributes to work in the field of operational measurement of Human Capabilities. Although a number of studies have examined the challenges posed in the measurement of Human Capabilities, there has not been a focus on the empirical merits of the methods and methodologies followed in identification and measurement of valuable capabilities especially in the Higher Education context. To this end, this study provides insights into the identification of valuable student capabilities through an exposition of the methods which can be followed to create and measure robust indicators of student capabilities. A quantitative inquiry determines which Human capabilities students in Higher Education institutions have reason to value and the results of this process are compared to a theoretical student capabilities literature. The thesis advocates for a human development approach over a human capital approach in evaluating the wellbeing of students. The study is significant in that it aids policy and decision makers in Higher Education to identify what students value and thus be in a position to fashion curricula, programmes and policies in a way which best benefits the subjects. To achieve the above mentioned goal, the thesis draws substantially on the work of Paul Anand, Amartya Sen, Flavio Comim, Enrica Chiappero Martinetti, Ingrid Robeyns, Melanie Walker and Sabina Alkire, among others, who have researched and advanced in the field of operational measurement of human capabilities in the Higher Education environment.
Open Access
Continuous-time Markov modelling of the effects of treatment regimens on HIV/AIDS immunology and virology
(University of the Free State, 2019) Shoko, Claris; Chikobvu, Delson
As the Human immunodeﬁciency virus (HIV) enters the human body, its main target is the CD4+ cell, which it turns into a factory that produces millions of other HIV particles, thus compromising the immune system and resulting in opportunistic infections, for example tuberculosis (TB). Combination Anti-retroviral therapy (cART) has become the standard of care for patients with HIV infection and has led to the reduction in acquired immunodeﬁciency syndrome (AIDS) related morbidity and mortality, an increase in CD4+ cell counts and a decrease in viral load count to undetectable levels. In modelling HIV/AIDS progression in patients, researchers mostly deal with either viral load only or CD4+cellcountsonly, as they expect these two variables to be collinear. The purpose of this study is to ﬁt a continuous-time Markov model that best describes mortality of HIV infected patients on cART by eventually including both CD4+ cell counts monitoring and viral load monitoring in a single model after treating for collinearity of these variables using the Principal Component approach. Acohortof320HIVinfectedpatientsoncARTfollowedupat a Wellness Clinic in Bela Bela, South Africa, is used in this thesis. These patients are administered with a triple therapy of two nucleoside reverse transcriptase inhibitor (NRTIs) and one non-nucleoside reverse transcriptase inhibitor (NNRTI). The thesis is divided into ﬁve sections. In the ﬁrst section, a continuous-time homogeneous Markov model based on CD4+ cell count states is ﬁtted. The model is used to analyse the effects of tuberculosis (TB) co-infection on the immunologic progression of HIV/AIDS patients on cART. TB co-infection was of interest because it is an opportunistic infection that takes advantage of the compromised immune system. Results from this section showed that once TB is diagnosed prior to treatment initiation and managed, mortality rates are reduced. However, if TB is diagnosed during the course of treatment, it increases the rates of immune deterioration in patients, leading to high rates of mortality. Therefore, this section proposes the need for routine TB screening before treatment initiation and a tevery stage of the follow up period, to avoid loss of lives. The goal of cART is not only to boost the immune system but also to suppress the viral load to undetectable levels. Thus, in the second section, a non-homogeneous continuous-time Markov model based on viral load states is ﬁtted. This model helped in revealing possibilities of viral rebound among patient son cART. Although there were no signiﬁcant gender differences on HIV/AIDS virology, the model explained the progression of patients better than the model based on CD4+ cell count ﬁtted in the ﬁrst section. In the third section, determinants of viral rebound are analysed. Viral rebound was notable mainly after patients had attained a viral load suppressed to the levels between 50 copies/mL and 10 000 copies/mL. The major attributes of viral rebound were non-adherence, lactic acid, resistance to treatment, and different combination therapy such as AZT-3TC-LPV/r and FTC-TDF-EFV. This section suggests the need to closely monitor HIV patients to ensure attainment of undetectable viral load (below 50 copies/mL) during the ﬁrst six months of treatment uptake, as this reduces chances of viral rebound, leading to life gain by HIV/AIDS patients. The fourth section compares the use of viral load count and CD4+cell count in monitoring HIV/AIDS disease progression on patients receiving cART in order to establish the superiority of viral load over CD4+ cell count. This was done by ﬁtting two separate models, one for CD4+ cell count states and the other one for viral load states. Comparison of the ﬁtted models were based on percentage prevalence plots for the ﬁtted model and for the observed data and likelihood ratio tests. The test conﬁrmed that viral load monitoring is superior compared to CD4+cell count monitoring. Viral load monitoring is very good at detecting virologic failure, thereby avoiding unnecessary switches of treatment lines. However, this section suggests the use of both CD4+cellcount monitoring and viral load monitoring because CD4+ cell count monitoring helps in managing possibilities of the development of opportunistic infections. In the ﬁfth section, continuous-time homogeneous Markov models are ﬁtted, including both CD4+ cell count monitoring and viral load monitoring in one model. Since these variables are assumed to be collinear, principal component analysis was used to treat for the collinearity among these two variables. The models are ﬁtted in such a way that when Markov states are based on CD4+ cell count, the principal component of viral load is included as a covariate, and when the Markov states are based on viral load, the principal component of CD4+cell count is included as a covariate. Results from the models show an improvement in the power of the continuous-time Markov model to explain and predict mortality when both CD4+cellcount and viral load routine monitoring are included in one model.
Open Access
Modelling and analysing risk in precious metals
(University of the Free State, 2018) Chinhamu, Knowledge; Chikobvu, Delson
The prices of precious metals are volatile and financial market participants are interested in knowing the downside of holding precious metals in their portfolios. Risk management tools such as Value-at-Risk (VaR) are highly dependent on the underlying distributional assumption. Identifying a distribution that may best capture all the aspects of the given financial data can provide immense advantages to both investors and risk managers. In the analysis and modelling of financial returns, there are stylised facts that are observed. These include volatility clustering, heavy-tails, asymmetry, conditional heavy tails and long range dependence (long memory). In this study, we investigated the stylised facts of gold, platinum and silver returns. We thus propose models that are able to capture their empirical features. The models capture extreme tails of profit and loss distributions and improve the estimation of Value-at-Risk (VaR) of precious metal prices returns. Firstly, we evaluate the performance of existing heavy-tailed and flexible distributions in modelling extreme risk for precious metal returns. The heavy-tailed and flexible distributions used are: Generalised Hyperbolic Distributions (GHDs), Generalised Lambda Distribution (GLD), Stable Distribution (SD), Generalised Pareto Distribution (GPD), Generalised Extreme Value Distribution (GEVD), Pearson type-IV Distribution (PIVD), Symmetrical Student-t Distribution (STD) and Skewed Studentt Distribution (SSTD). Secondly, we couple ARMA-GARCH models and ARMAAPARCH models with heavy-tailed and flexible distributions. We fit the models to precious metal returns and evaluate their relative performance in estimating Valueat-Risk (VaR) using a number of conditional assumptions. The proposed models performed favourably when compared with the APARCH models with a Student-t distribution and the APARCH models with a skewed Student-t distribution usually used in the literature. This provides financial analysts with an alternative distributional scheme to be used in economic modelling. Thirdly, because all daily precious metal price returns exhibit volatility clustering, heavy tails, asymmetry and long range dependence, we fit the long-memory GARCH models under the GHDs, the GPD, the GEVD, the SD, the STD, the SSTD, the GLD and the PIVD assumptions to our price return data. The Anderson-Darling test is used to check for model adequacy. Kupiec likelihood ratio tests and Christoffersen conditional coverage tests are also used in this study to evaluate objectively whether VaR model is adequate. The backtesting results confirm that the long-memory GARCH-heavy-tailed models are adequate for improving risk management assessments and hedging strategies in the highly volatile metal markets. ARFIMA-HYGARCH, ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with PIVD, Normal-Inverse Gaussian Distribution (NIGD), full GHD, FMKL GLD and Generalised Hyperbolic Student-t Distribution (GHStD) innovations are found to be suitable for VaR estimation of precious metals, thereby providing a good alternative candidate for modelling financial returns.
Open Access
Modelling electricity demand in South Africa
(University of the Free State, 2014-01) Sigauke, Caston; Chikobvu, Delson
English: Peak electricity demand is an energy policy concern for all countries throughout the world, causing blackouts and increasing electricity tariffs for consumers. This calls for load curtailment strategies to either redistribute or reduce electricity demand during peak periods. This thesis attempts to address this problem by providing relevant information through a frequentist and Bayesian modelling framework for daily peak electricity demand using South African data. The thesis is divided into two parts. The first part deals with modelling of short term daily peak electricity demand. This is done through the investigation of important drivers of electricity demand using (i) piecewise linear regression models, (ii) a multivariate adaptive regression splines (MARS) modelling approach, (iii) a regression with seasonal autoregressive integrated moving average (Reg-SARIMA) model (iv) a Reg-SARIMA model with generalized autoregressive conditional heteroskedastic errors (Reg-SARIMA-GARCH). The second part of the thesis explores the use of extreme value theory in modelling winter peaks, extreme daily positive changes in hourly peak electricity demand and same day of the week increases in peak electricity demand. This is done through fitting the generalized Pareto, generalized single Pareto and the generalized extreme value distributions. One of the major contributions of this thesis is quantification of the amount of electricity which should be shifted to off peak hours. This is achieved through accurate assessment of the level and frequency of future extreme load forecasts. This modelling approach provides a policy framework for load curtailment and determination of the number of critical peak days for power utility companies. This has not been done for electricity demand in the context of South Africa to the best of our knowledge. The thesis further extends the autoregressive moving average-exponential generalized autoregressive conditional heteroskedasticity model to an autoregressive moving average exponential generalized autoregressive conditional heteroskedasticity-generalized single Pareto distribution. The benefit of this hybrid model is in risk modelling of under and over demand predictions of peak electricity demand. Some of the key findings of this thesis are (i) peak electricity demand is influenced by the tails of probability distributions as well as by means or averages, (ii) electricity demand in South Africa rises significantly for average temperature values below 180C and rises slightly for average temperature values above 220C and (iii) modelling under and over demand electricity forecasts provides a basis for risk assessment and quantification of such risk associated with forecasting uncertainty including demand variability.
Open Access
Modelling international tourist arrivals volatility in Zimbabwe using a GARCH process
(AfricaJournals, 2021) Makoni, Tendi; Chikobvu, Delson
The aim of the paper was to develop bootstrap prediction intervals for international tourism demand and volatility in Zimbabwe after modelling with an ARMA-GARCH process. ARMA-GARCH models have better forecasting power and are capable of capturing and quantifying volatility. Bootstrap prediction intervals can account for future uncertainty that arises through parameter estimation. The monthly international tourism data obtained from the Zimbabwe Tourism Authority (ZTA) (January 2000 to June 2017) is neither seasonal nor stationary and is made stationery by taking a logarithm transformation. An ARMA(1,1) model fits well to the data; with forecasts indicating a slow increase in international tourist arrivals (outside of the Covid-19 period). The GARCH(1,1) process indicated that unexpected tourism shocks will significantly impact the Zimbabwe international tourist arrivals for longer durations. Volatility bootstrap prediction intervals indicated minimal future uncertainty in international tourist arrivals. For the Zimbabwe tourism industry to remain relevant, new tourism products and attraction centres need to be developed, as well as embarking on effective marketing strategies to lure even more tourists from abroad. This will go a long way in increasing the much-needed foreign currency earnings needed to revive the Zimbabwean economy.
Open Access
Quantile regression analysis of modifiable and non-modifiable predictors of stroke among adults in South Africa
(Bentham Open, 2021) Chikobvu, Delson; Matizirofa, Lynn's
Background: Stroke is the second largest cause of mortality and long-term disability in South Africa (SA). Stroke is a multifactorial disease regulated by modifiable and non-modifiable predictors. Little is known about the stroke predictors in SA, particularly modifiable and non-modifiable. Identification of stroke predictors using appropriate statistical methods can help formulate appropriate health programs and policies aimed at reducing the stroke burden. This study aims to address important gaps in stroke literature i.e., identifying and quantifying stroke predictors through quantile regression analysis. Methods: A cross-sectional hospital-based study was used to identify and quantify stroke predictors in SA using 35730 individual patient data retrieved from selected private and public hospitals between January 2014 and December 2018. Ordinary logistic regression models often miss critical aspects of the relationship that may exist between stroke and its predictors. Quantile regression analysis was used to model the effects of each predictor on stroke distribution. Results: Of the 35730 cases of stroke, 22183 were diabetic. The dominant stroke predictors were diabetes, hypertension, heart problems, the female gender, higher age groups and black race. The age group 55-75 years, female gender and black race, had a bigger effect on stroke distribution at the lower upper quantiles. Diabetes, hypertension and cholesterol showed a significant impact on stroke distribution (p < 0.0001). Conclusion: Most strokes are attributable to modifiable factors. Study findings will be used to raise awareness of modifiable predictors to prevent strokes. Regular screening and treatment are recommended for high-risk individuals with identified predictors in SA.
Open Access
A survey on participation and attitude to sports among undergraduate students in junior residences at the University of the Free State
(University of the Free State, 2016-01) Mangoejane, Patricia Kekeletso; Chikobvu, Delson
The main objective of this study is to assess and quantify participation in sporting activities by students and to determine the factors influencing students’ intentions to participate or not to participate in sports at the University of the Free State. The data are obtained from interviewing students participating or not participating in various sporting codes available at the University of the Free State (main campus in Bloemfontein, South Africa). A systematic random sampling technique was used as the interviewing team knocked on every fifth door in a given residence to ensure that all corners of each residence were reached. The students found at the residence at that particular time, were asked to fill in the questionnaire. Tables and charts are used for illustration of results. T-tests, F-tests, Principal component analysis, Cluster comparison analysis and Item analysis are also performed for further analysis. Three hundred and eight students (308) (61% females and 39% males) living in junior residences were interviewed for this research. The majority of participants (75%) were non-whites (blacks, coloured, and Asians); this was in line with the University of the Free State enrolment structure of the year 2011 (75% non-whites and 25% whites). The reasons provided by the participants for their participation in sporting activities were indicated as keeping fit (91%), releasing of stress (89.35%), gaining a feeling of wellbeing (83%), increasing in physical abilities (81%) and previous school sports involvement (67%). Students from second academic year upwards mostly raised the positive response that they relied on regular exercise to achieve academic success. The researcher concludes that certain variables, namely gender, age group, race, marital status preferred language of study, faculty of study, academic year of study, previous school sport participation, current sport participation, participated sporting codes, reasons for sport participation and reasons for non-sport participation for students, are the most important variables that the Kovsie Sport and management of sports, should focus on in order to encourage students to participate in sporting activities. Through sports, students are also able to interact with one another and participate in different sporting codes offered by the university.

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