Research Articles (Statistics and Actuarial Science)

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Basic in-mouth attribute evaluation : a comparison of two panels
(MDPI, 2018-12-21) Mihnea, Mihaela; Aleixandre-Tudo, Jose Luis; Kidd, Martin; Du Toit, Wessel
Astringency is often difficult to evaluate accurately in wine because of its complexity. This accuracy can improve through training sessions, but it can be time-consuming and expensive. A way to reduce these costs can be the use of wine experts, who are known to be reliable evaluators. Therefore, the aim of this work was to compare the sensory results and the panel performance obtained using trained panelists versus wine experts (winemakers). Judges evaluated twelve red wines for in-mouth basic perception (sweet, sour, bitter, astringent, and burning sensation) following the same tasting protocol and with the samples being presented in two different tasting modalities. Panels’ performance and relationship between the chemical composition and the sensory perception were investigated. Both panels showed similar consistency and repeatability, and they were able to accurately measure the astringency of the wines. However, the significant correlations between sensory scores and chemical composition varied with the panel and the tasting modality. From our results, we could see that winemakers tended to discriminate better between the samples when the differences were very small.
Bayesian highest posterior density intervals for the availability of a system with a 'rest-period' for the repair facility
(SAIIE, 2001) Yadavalli, V. S. S.; Bekker, A.; Mostert, P. J.; Botha, M.
In this paper Bayesian estimation for the steady state availability of a one-unit system with a rest-period for the repair facility is studied. The assumption is that the repair facility takes rest with probability p after each repair completion and the facility does not take the same with probability (l - p). The prior information is assumed to be vague and the Jeffreys' prior is used for the unknown parameters in the system. Gibbs sampling is used to derive the posterior distribution of the availability and subsequently the highest posterior density (HPD) intervals. A numerical example illustrates these results.
The bells of the Stellenbosch Moederkerk
(Church History Society of Southern Africa, 2018) De Wet, Tertius; Teugels, Jef L.; Van Deventer, Pieta
The Dutch Reformed Moederkerk of Stellenbosch has a long history, being the second oldest congregation of the Dutch Reformed Church in South Africa. The history of the church has been well documented, including the architecture and building of the church buildings over its 332 years of existence. However, although bells have from the beginning played an important part in the church's history, very little has been written on the bells. This paper reports on research carried out into that important aspect of the church's life, in that way adding to Moederkerk's recorded history.
Berekening van a posteriori-verdeling in Bayes-analise : toepassing in 'n betroubareheidstelsel wat afwisselend gebruik word
(AOSIS, 2002) Yadavalli, V. S. S.; Mostert, P. J.; Bekker, A.; Botha, M.
Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.
Calculation aspects of the European rebalanced basket option using Monte Carlo methods : valuation
(Operations Research Society of South Africa, 2012) Van der Merwe, C. J.; Conradie, W. J.
Extra premiums can be charged to a client to guarantee a minimum payout of a contract on a portfolio that gets rebalanced on a regular basis back to fixed proportions. The valuation of this premium can be changed to that of the pricing of a European put option with underlying rebalanced portfolio. This article finds the most efficient estimators for the value of this path-dependant multi-asset put option using different Monte Carlo methods. With the help of a refined method, computing time of the value decreased significantly. Furthermore, Variance Reduction Techniques and Quasi-Monte Carlo methods delivered more accurate and faster converging estimates as well.
Catastrophe modelling : deriving the 1-in-200 year mortality shock for a South African insurer’s capital requirements under solvency assessment management
(Actuarial Society of South Africa, 2015) Plantinga, A. A.; Corubolo, D. J.; Clover, R. J.
This paper investigates catastrophe risk for South African life insurers by considering the additional deaths that could arise from a 1-in-200 year mortality shock. Existing South African academic research on catastrophic risk has mostly focused on property losses and the resulting impact on property insurance companies. Life catastrophe risks have not been extensively modelled in a South African context. Local research would be beneficial in terms of quantifying these catastrophic risks for South African life insurers, and would assist firms when assessing their own catastrophe mortality solvency requirements under the new Solvency Assessment and Management (SAM) regime by providing a summary of data relating to various past catastrophes. In this paper we model a wide range of catastrophes to assess such mortality risk faced by life insurance companies in South Africa. An extensive exercise was undertaken to obtain data for a wide range of catastrophes and these data were used to derive severity and frequency distributions for each type of catastrophe. Data relating to global events were used to supplement South African data where local data were sparse. Data sources included official government statistics, industry reports and historical news reports. Since, by nature, catastrophic events are rare, little data are available for certain types of catastrophe. This means there is a large degree of uncertainty underlying some of the estimates. Simulation techniques were used to derive estimated distributions for the potential number of deaths for particular catastrophic events. The calculated overall shock for the national population was 2.6 deaths per thousand, which was lower than the SAM Pillar 1 shock of 3.2 deaths per thousand for the same population. It has been found that a worldwide pandemic is by far the main risk in terms of number of deaths in a catastrophe and, given that this is the most significant component of catastrophe risk, prior research on this risk in an South African context is summarised and revisited.
Changes in mortality of people living with HIV in South Africa and their potential implications for life assurers
(Actuarial Society of South Africa, 2016) Strydom, M. L.; Corubolo, D.; Nel, C.
This research investigates the impact of improved (and improving) mortality experience in South Africa as a result of the increased (and increasing) access to antiretroviral treatment on South African life assurers, the entry-level insurance market and the wider South African economy. The research focuses on various potential impacts on the entry-level insurance market, including new business profitability, product development and pricing, market penetration and the potential for increased savings. This research has been done with the assistance of four of the main South African life offices and also draws on the new THEMBISA AIDS model on which a working paper has been produced. The research is based on the THEMBISA model in order to investigate the potential impact of alternative mortality scenarios on typical entry-level products within the industry where the scenarios have been based on actual current and proposed antiretroviral roll-out strategies by the Department of Health. Potential improvements to profitability, premium reductions, benefit enhancements and cashback benefits are quantified using a profit test model for entry-level market products.
Comparison of zero replacement strategies for compositional data with large numbers of zeros
(Elsevier B.V., 2021-03) Lubbe, Sugnet; Filzmoser, Peter; Templ, Matthias
Modern applications in chemometrics and bioinformatics result in compositional data sets with a high proportion of zeros. An example are microbiome data, where zeros refer to measurements below the detection limit of one count. When building statistical models, it is important that zeros are replaced by sensible values. Different replacement techniques from compositional data analysis are considered and compared by a simulation study and examples. The comparison also includes a recently proposed method (Templ, 2020) [1] based on deep learning. Detailed insights into the appropriateness of the methods for a problem at hand are provided, and differences in the outcomes of statistical results are discussed.
Does money "buy" tolerance toward damage-causing wildlife?
(Wiley, 2020-07-26) Kansky, Ruth; Kidd, Martin; Fischer, Joern
The Kavango-Zambezi Transfrontier Conservation Area supports large-scale migrations of wildlife that occur in a mixed agri-conservation landscape in five Southern African countries. Human–Wildlife Conflict is a key challenge and understanding the drivers of communities' willingness to coexist with wildlife is thus critical. Community based natural resource management (CBNRM) is a widely used economic approach to foster human-wildlife coexistence with the assumption that monetary benefits can “buy” tolerance by offsetting the disservices of living with wildlife. We tested this assumption and hypothesized that Namibians would be more tolerant towards wildlife than Zambians because they received higher monetary benefits from wildlife. We used the Wildlife Tolerance Model (WTM) as the framework to define tolerance and identify tolerance drivers. We found Namibians tolerance was higher for lion, elephant and hyena but not for kudu and baboon. After controlling for confounding variables of the WTM that could potentially explain differences in tolerance, contrary to expectation, the monetary benefits did not account for higher Namibian tolerance. Instead, only nonmonetary benefits explained the higher tolerance. We used crowding theory to explain this finding, proposing that CBNRM in Namibia and the monetary benefits from the program “crowd in” intrinsic motivation to appreciate and tolerate wildlife.
An easy and low cost option for economic statistical process control using Excel
(Operations Research Society of South Africa, 2009) Van Deventer, P. J. U.; Manna, Z. G.
ENGLISH SUMMARY : In this paper, a user-friendly, Excel program is developed to search for the optimal values of the parameters in minimizing the total cost function in both economic and economic statistical designs of the X-control chart. Two assumptions are considered in the development and use of the economic or economic statistical models. These assumptions are potentially critical. It is assumed that the time between process shifts can be modelled by means of the exponential distribution. It is further assumed that there is only one assignable cause. Based on these assumptions, economic or economic statistical models are derived using a total cost function per unit time as proposed by a unified approach. In this approach the relationship between the three-control chart parameters as well as the three types of costs are expressed in the total cost function. The optimal parameters are usually obtained by the minimization of the expected total cost per unit time. Nevertheless, few practitioners have tried to optimize the design of their X-control charts. One reason for this is that the cost models and their associated optimization techniques are often too complex and di cult for practitioners to understand and apply. Therefore, a user-friendly Excel program has been developed in this paper and the numerical examples illustrated are executed on this program. The optimization procedure is easy-to-use, easy-to-understand, and easy-to-access. Moreover, and not least important, it is a low cost option unlike previous approaches which can be found in expensive software packages only. The results and the execution times of all numerical examples show that our optimization procedure using Excel is accurate and efficient.
Equity- and entity-based multiples in emerging markets : evidence from the JSE Securities Exchange
(Clute Institute, 2013-05) Nel, W. S.; Bruwer, B. W.; Le Roux, N. J.
Analysts typically distinguish between equity- and entity-based approaches when employing the free cash flow model to perform equity valuations. However, when multiples are used to perform equity valuations, analysts often neglect to distinguish between equity- and entity-based approaches. In addition, limited empirical evidence exists on the relative valuation performance of equity- and entity-based multiples in developed capital markets and the emerging markets literature is entirely silent in this regard. In this paper the valuation accuracy of equity-based multiples is compared to that of entity-based multiples in valuing the equity of South African companies listed on the JSE Securities Exchange for the period 2001-2010. The research results reveal that equity-based multiples significantly outperform entity-based multiples, indicating a potential increase in valuation accuracy of as much as 15.37%.
Extending a scatterplot for displaying group structure in multivariate data : a case study
(Operations Research Society of South Africa, 2005) Gardner, S.; Le Roux, N. J.; Rypstra, T.; Swart, J. P. J.
ENGLISH SUMMARY : The power of canonical variate analysis (CVA) biplots, when regarded as extensions of or- dinary scatterplots to describe variation and group structure in multivariate observations, is demonstrated by presenting a case study from the South African wood pulp industry. It is shown how multidimensional standards specified by users of a product may be added to the biplot in the form of acceptance regions such that the roles of the respective variables that influence the product can be ascertained. The case study considers an alternative to CVA and multivariate analysis of variance (MANOVA) when the application of these procedures becomes questionable as a result of dealing with small sample sizes and heterogeneity of covariance matrices. It is explained how analysis of distance (AOD) analogous to analysis of variance may be performed in such cases. Biplots to accompany AOD are provided. The biplots and AOD illustrated in the case study from the wood pulp industry have the potential to be used widely where a primary product, influenced by several variables, is produced and where this product is of importance to various secondary manufacturers depending on which set of multidimensional specifications are met.
Fermentation-derived aroma compounds in varietal young wines from South Africa
(SASEV, 2010-09) Louw, L.; Tredoux, A. G. J.; Van Rensburg, P.; Kidd, M.; Naes, T.; Nieuwoudt, Helene
The volatile composition of 925 single cultivar young Sauvignon blanc, Chardonnay, Pinotage, Merlot, Shiraz and Cabernet Sauvignon wines of vintages 2005 to 2007, was determined using gas chromatography-flame ionisation detection. Compositional data were compared to published data on young wines from South Africa and other countries. South African young wines analysed in this study had a largely similar volatile composition to that reported in the literature. Significant between-vintage and between-cultivar differences were observed in the volatile composition of the wines investigated in this study. The concentration ranges of four compounds in red wines, hexanol, propanol, diethyl succinate and ethyl lactate, and four compounds in white wines, 2-phenylethanol, hexanoic acid, isoamyl acetate and propanol, were not influenced by vintage effects. This finding was interpreted as the first indication that typical concentration ranges for some aroma compounds can be established for South African young cultivar wines. A trend was observed in the white wines that the alcohols and their respective acetate esters, as well as fatty acids and their ethyl esters, were responsible for the vintage-related effects. Differences in volatile composition between Chardonnay and Sauvignon blanc wines could also largely be explained on the same basis. Classification models were established to discriminate between individual red wine cultivars and between the two white wine cultivars and correct classification rates of respectively, 79 % and 85 % were achieved.
Flexible graphical assessment of experimental designs in R : the vdg package
(Foundation for Open Access Statistics, 2016-10) Schoonees, Pieter; Le Roux, Niel; Coetzer, Roelof
The R package vdg provides a flexible interface for producing various graphical summaries of the prediction variance associated with specific linear model specifications and experimental designs. These methods include variance dispersion graphs, fraction of design space plots and quantile plots which can assist in choosing between a catalogue of candidate experimental designs. Instead of restrictive optimization methods used in traditional software to explore design regions, vdg utilizes sampling methods to introduce more flexibility. The package takes advantage of R's modern graphical abilities via ggplot2 (Wickham 2009), adds facilities for using a variety of distance methods, allows for more flexible model specifications and incorporates quantile regressions to help with model comparison.
Historic bells in Moravian Missions in South Africa's Western Cape
(Historical Association of South Africa, 2014-11) De Wet, Tertius; Teugels, Jef L.; Van Deventer, Pieta
The Moravian Church was the first denomination to begin with missionary work among the indigenous people in South Africa and today the church still has a very strong presence in the country. After opening their first mission at Genadendal in 1738, a number of further mission stations were established during the nineteenth century in the Western Cape. These missionary stations played an extremely important part in the lives of their residents, both spiritually and socially. In the Moravian Church, as in other churches, their church buildings and the bells accompanying them form an integral part of their heritage. Despite the research that has been carried out on the mission stations per se, no systematic research has been done on the bells at these stations. In this article we discuss these bells, when and where they came from, and who made them. Due to the historical value of these mission stations, we cannot consider the bells without some background discussion of the stations' history. A brief historical background is provided for each station before focusing on the bells at that station and who cast them. Finally, a number of areas for further research are touched upon.
HIV-exposure, early life feeding practices and delivery mode impacts on faecal bacterial profiles in a South African birth cohort
(Nature Research, 2018) Claassen-Weitz, Shantelle; Gardner-Lubbe, Sugnet; Nicol, Paul; Botha, Gerrit; Mounaud, Stephanie; Shankar, Jyoti; Nierman, William C.; Mulder, Nicola; Budree, Shrish; Zar, Heather J.; Nicol, Mark P.; Kaba, Mamadou
There are limited data on meconium and faecal bacterial profiles from African infants and their mothers. We characterized faecal bacterial communities of infants and mothers participating in a South African birth cohort. Stool and meconium specimens were collected from 90 mothers and 107 infants at birth, and from a subset of 72 and 36 infants at 4–12 and 20–28 weeks of age, respectively. HIV-unexposed infants were primarily exclusively breastfed at 4–12 (49%, 26/53) and 20–28 weeks (62%, 16/26). In contrast, HIV-exposed infants were primarily exclusively formula fed at 4–12 (53%; 10/19) and 20–28 weeks (70%, 7/10). Analysis (of the bacterial 16S rRNA gene sequences of the V4 hypervariable region) of the 90 mother-infant pairs showed that meconium bacterial profiles [dominated by Proteobacteria (89%)] were distinct from those of maternal faeces [dominated by Firmicutes (66%) and Actinobacteria (15%)]. Actinobacteria predominated at 4–12 (65%) and 20–28 (50%) weeks. HIV-exposed infants had significantly higher faecal bacterial diversities at both 4–12 (p = 0.026) and 20–28 weeks (p = 0.002). HIV-exposed infants had lower proportions of Bifidobacterium (p = 0.010) at 4–12 weeks. Maternal faecal bacterial profiles were influenced by HIV status, feeding practices and mode of delivery. Further longitudinal studies are required to better understand how these variables influence infant and maternal faecal bacterial composition.
Host markers in Quantiferon supernatants differentiate active TB from latent TB infection : preliminary report
(BioMed Central, 2009-05) Chegou, Novel N.; Black, Gillian F.; Kidd, Martin; Van Helden, Paul D.; Walzl, Gerhard
Background: Interferon gamma release assays, including the QuantiFERON® TB Gold In Tube (QFT) have been shown to be accurate in diagnosing Mycobacterium tuberculosis infection. These assays however, do not discriminate between latent TB infection (LTBI) and active TB disease. Methods: We recruited twenty-three pulmonary TB patients and 34 household contacts from Cape Town, South Africa and performed the QFT test. To investigate the ability of new host markers to differentiate between LTBI and active TB, levels of 29 biomarkers in QFT supernatants were evaluated using a Luminex multiplex cytokine assay. Results: Eight out of 29 biomarkers distinguished active TB from LTBI in a pilot study. Baseline levels of epidermal growth factor (EGF) soluble CD40 ligand (sCD40L), antigen stimulated levels of EGF, and the background corrected antigen stimulated levels of EGF and macrophage inflammatory protein (MIP)-1β were the most informative single markers for differentiation between TB disease and LTBI, with AUCs of 0.88, 0.84, 0.87, 0.90 and 0.79 respectively. The combination of EGF and MIP-1β predicted 96% of active TB cases and 92% of LTBIs. Combinations between EGF, sCD40L, VEGF, TGF-α and IL-1α also showed potential to differentiate between TB infection states. EGF, VEGF, TGF-α and sCD40L levels were higher in TB patients. Conclusion: These preliminary data suggest that active TB may be accurately differentiated from LTBI utilizing adaptations of the commercial QFT test that includes measurement of EGF, sCD40L, MIP-1β, VEGF, TGF-α or IL-1α in supernatants from QFT assays. This approach holds promise for development as a rapid diagnostic test for active TB.
Identifying secondary series for stepwise common singular spectrum analysis
(Operations Research Society of South Africa, 2013) Viljoen, H.; Steel, S. J.
Common singular spectrum analysis is a technique which can be used to forecast a primary time series by using the information from a secondary series. Not all secondary series, however, provide useful information. A first contribution in this paper is to point out the properties which a secondary series should have in order to improve the forecast accuracy of the primary series. The second contribution is a proposal which can be used to select a secondary series from several candidate series. Empirical studies suggest that the proposal performs well.
The impact of behavioural economics and finance on retirement provision
(Actuarial Society of South Africa, 2016) Van Zyl, N.; Van Zyl, D. J. J.
The significant shift from defined benefit to defined contribution retirement funds in South Africa has led to many fund members bearing responsibility for a range of risks. Many of these risks, such as those related to investment, longevity and cognitive deterioration are unavoidable. Another category of risk is that related to the choices made by government, employers, trustees, advisors and/or individuals at either national, scheme or individual level. These choices may also pose a threat to a member’s financial wellbeing in retirement. Behavioural economics and finance helps to explain the choices made by these stakeholders in the retirement industry. The authors explain this concept in the context of industry stakeholders and the unique South African economic and demographic landscape, focusing on defined contribution retirement funds. Key behavioural insights applicable to the retirement industry are explored and, where practical, illustrated by stakeholder behaviour. Possible ways to harness these insights in order to improve retirement wellbeing are then discussed.
The impact of industry classification on the valuation accuracy of multiples in the South African capital market
(The Clute Institute, 2013-01) Nel, Soon; Bruwer, Wilna; Le Roux, Niel
Although multiples are used extensively in practice, empirical guidance in emerging markets is limited in this regard. In terms of valuation accuracy, the impact of peer group selection by way of industry classification in emerging markets has not yet been substantiated by research. This paper investigates the valuation performance of multiples over various industry classifications when valuing the equity of South African companies listed on the Johannesburg Stock Exchange for the period 2001 to 2010. The empirical results revealed that peer group selection based on a narrower industry classification could, on average, increase valuation accuracy by as much as 19.60%.

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