Philosophiae Doctor - PhD (Statistics and Population Studies)
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Item Analysis and estimation of customer survival Time in subscription-based businesses(University of the Western Cape, 2008) Mohammed, Zakariya Mohammed Salih; Kotze, Danelle; Maritz, Johannes Stefan; Dept. of Statistics; Faculty of ScienceSubscription-based industries have seen a massive expansion in recent decades. In this type of industry the customer has to subscribe to be able to enjoy the service; there-fore, well-de ned start and end points of the customer relationship with the service provider are known. The length of this relationship, that is the time from subscription to service cancellation, is de ned as customer survival time. Unlike transaction-based businesses, where the emphasis is on the quality of a product and customer acquisition, subscription-based businesses focus on the customer and customer retention. A customer focus requires a new approach: managing according to customer equity (the value of a rm's customers) rather than brand equity (the value of a rm's brands). The concept of customer equity is attractive and straightforward, but the implementation and management of the customer equity approach do present some challenges. Amongst these challenges is that customer asset metric - customer lifetime value (the present value of all future pro ts generated from a customer) - depends upon assumptions about the expected survival time of the customer (Bell et al., 2002; Gupta and Lehmann, 2003). In addition, managing and valuing customers as an asset require extensive data and complex modelling. The aim of this study is to illustrate, adapt and develop methods of survival analysis in analysing and estimating customer survival time in subscription-based businesses. Two particular objectives are studied. The fi rst objective is to rede ne the existing survival analysis techniques in business terms and to discuss their uses in order to understand various issues related to the customer-fi rm relationship. The lesson to be learnt here is the ability of survival analysis techniques to extract important information on customers with regard to their loyalties, risk of cancellation of the service, and lifetime value. The ultimate outcome of this process of studying customer survival time will be to understand the dynamics and behaviour of customers with respect to their risk of cancellation, survival probability and lifetime value. The results of the estimates of customer mean survival time obtained from different nonparametric and parametric approaches; namely, the Kaplan-Meier method as well as exponential, Weibull and gamma regression models were found to vary greatly showing the importance of the assumption imposed on the distribution of the survival time. The second objective is to extrapolate the customer survival curve beyond the empirical distribution. The practical motivation for extrapolating the survival curve beyond the empirical distribution originates from two issues; that of calculating survival probabilities (retention rate) beyond the empirical data and of calculating the conditional survival probability and conditional mean survival time at a speci c point in time and for a speci c time window in the future. The survival probabilties are the main components needed to calculate customer lifetime value and thereafter customer equity. In this regard, we propose a survivor function that can be used to extrapolate the survival probabilities beyond the last observed failure time; the estimation of parameters of the newly proposed extrapolation function is based completely on the Kaplan-Meier estimate of the survival probabilities. The proposed function has shown a good mathematical accuracy. Furthermore, the standard error of the estimate of the extrapolation survival function has been derived. The function is ready to be used by business managers where the objective is to enhance customer retention and to emphasise a customer-centric approach. The extrapolation function can be applied and used beyond the customer survival time data to cover clinical trial applications. In general the survival analysis techniques were found to be valuable in understanding and managing a customer- rm relationship; yet, much still needs to be done in this area of research to make these techniques that are traditionally used in medical studies more useful and applicable in business settings.Item Contraception and unmet-needs in Africa(University of the Western Cape, 2009) Stiegler, Nancy; Dept. of Statistics; Faculty of ScienceThe first objective of this study is to show if diffusion of contraception in areas of traditional high fertility has gone through profound changes. Indeed, we would like to know if contraceptive behaviours have evolved because of new fertility perceptions and also because partners now have greater freedom to make choices in a relationship. The second objective of this study is not only to highlight the levels and trends of contraception and the factors influencing their use (government policies, role of family planning, etc.) in developing countries, but also to consider the population of unmet-needs of contraception. Indeed, the level of contraceptive use depends obviously on users, but also on non-users with no needs and non-users with unsatisfied needs. The understanding of this last category of females is essential to a more accurate estimation of contraception levels, and, therefore for the estimation of fertility levels. This study analyses the contraceptive use in several developing countries in Africa and highlights the unsatisfied needs of contraception, to understand why such needs exist. To do so, we shall analyse available demographic data for thirty-five African countries by using the available Demographic and Health Surveys (DHS), from the 1980's to 2000's considering the DHS I, DHS II, DHS III and DHS IV. This great variety of surveys, seventy-nine in total, permits one to compare levels of contraception and 'unmet-needs' from country to country. The surveys also, make it possible to compare the evolution over time of specific countries or specific regions, and to subsequently comprehend the determining factors of contraceptive use or non-use.Item A framework for evaluating an introductory statistics programme at the University of the Western Cape(University of the Western Cape, 2009) Makapela, Nomawabo; Kotze, Danelle; Dept. of Statistics; Faculty of ScienceThere have been calls both from the government and private sector for Higher Education institutions to introduce programmes that produce employable graduates whilst at the same time contributing to the growing economy of the country by addressing the skills shortage. Transformation and intervention committees have since been introduced to follow the extent to which the challenges are being addressed (DOE, 1996; 1997; Luescher and Symes, 2003; Forbes, 2007). Amongst the list of issues that needed urgent address were the skills shortage and underperformance of students particularly university entering students (Daniels, 2007; De Klerk, 2006; Cooper, 2001). Research particularly in the South African context, has revealed that contributing to the underperformance of university entering students and shortage of skills are: the legacy of apartheid (forcing certain racial groups to focus on selected areas such as teaching and nursing), the schooling system (resulting in university entering students to struggle), the home language and academic language. Barrell (1998), places stress on language as a contributing factor towards the performance of students. Although not much research has been done on skills shortage, most of the areas with skills shortage require Mathematics, either on a minimum or comprehensive scale. Students who have a strong Mathematics background have proved to perform better compared to students who have a limited or no Mathematics background at all in Grade 12 (Hahn, 1988; Conners, McCown & Roskos-Ewoldsen, 1998; Nolan, 2002).The department of Statistics offers an Introductory Statistics (IS) course at first year level. Resources available to enhance student learning include: a problem-solving component with web-based tutorials and students attending lectures three hours per week. The course material and all the necessary information regarding the course including teach yourself problems, useful web-sites and links students can make use of, are all stored under the Knowledge- Environment for Web-based learning (KEWL). Despite all the available information, the students were not performing well and they were not interested in the course. The department regards statistical numeracy as a life skill. The desire of the department is to break down the fear of Statistics and to bring about a perspective change in students' mindsets. The study was part of a contribution to ensuring that the department has the best first year students in Statistics in the Western Cape achieving a success rate comparable to the national norm.