Global spread of infectious disease threatens the well-being of human, domestic, and wildlife health. A proper understanding of global distribution of these diseases is an important part of disease management and policy making. However, data are subject to complexities by heterogeneity across host classes and space-time epidemic processes [Waller et al., 1997, Hosseini et al., 2006]. The use of frequentist methods in Biostatistics and epidemiology are common and are therefore extensively utilized in answering varied research questions. In this thesis, we proposed the Hierarchical Bayesian approach to study the spatial and the spatio-temporal pattern of tuberculosis in Kenya [Knorr-Held et al., 1998, Knorr-Held, 1999, L opez-Qu lez and Munoz, 2009, Waller et al., 1997, Julian Besag, 1991]. Space and time interaction of risk (ψ[ij]) is an important factor considered in this thesis. The Markov Chain Monte Carlo (MCMC) method via WinBUGS and R packages were used for simulations [Ntzoufras, 2011, Congdon, 2010, David et al., 1995, Gimenez et al., 2009, Brian, 2003], and the Deviance Information Criterion (DIC), proposed by [Spiegelhalter et al., 2002], used for models comparison and selection. Variation in TB risk is observed among Kenya counties and clustering among counties with high TB relative risk (RR). HIV prevalence is identified as the dominant determinant of TB. We found clustering and heterogeneity of risk among high rate counties and the overall TB risk is slightly decreasing from 2002-2009. Interaction of TB relative risk in space and time is found to be increasing among rural counties that share boundaries with urban counties with high TB risk. This is as a result of the ability of models to borrow strength from neighbouring counties, such that near by counties have similar risk. Although the approaches are less than ideal, we hope that our formulations provide a useful stepping stone in the development of spatial and spatio-temporal methodology for the statistical analysis of risk from TB in Kenya. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

To investigate the effect of environmental pollution on the health of children in the Durban South Industrial Basin (DSIB) due to its proximity to industrial activities, 233 children from five primary schools were considered. Three of these schools were located in the south of Durban while the other two were in the northern residential areas that were closer to industrial activities. Data collected included the participants' demographic, health, occupational, social and economic characteristics. In addition, environmental information was monitored throughout the study specifically, measurements on the levels of some ambient air pollutants. The objective of this thesis is to investigate which of these factors had an effect on the lung function of the children. In order to achieve this objective, different sample survey data analysis techniques are investigated. This includes the design-based and model-based approaches. The nature of the survey data finally leads to the longitudinal mixed model approach. The multicolinearity between the pollutant variables leads to the fitting of two separate models: one with the peak counts as the independent pollutant measures and the other with the 8-hour maximum moving average as the independent pollutant variables. In the selection of the fixed-effects structure, a scatter-plot smoother known as the loess fit is applied to the response variable individual profile plots. The random effects and the residual effect are assumed to have different covariance structures. The unstructured (UN) covariance structure is used for the random effects, while using the Akaike information criterion (AIC), the compound symmetric (CS) covariance structure is selected to be appropriate for the residual effects. To check the model fit, the profiles of the fitted and observed values of the dependent variables are compared graphically. The data is also characterized by the problem of intermittent missingness. The type of missingness is investigated by applying a modified logistic regression model missing at random (MAR) test. The results indicate that school location, sex and weight are the significant factors for the children's respiratory conditions. More specifically, the children in schools located in the northern residential areas are found to have poor respiratory conditions as compared to those in the Durban-South schools. In addition, poor respiratory conditions are also identified for overweight children. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2006.

Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted penalty function not only provides a systematic platform to jointly analyze various quantities of interest, but also offers the convenience to extract key pieces of information from a risk management perspective. For example, by eliminating the penalty function, the Gerber-Shiu function becomes the Laplace-Stieltjes transform of the time to ruin, inversion of which results in a series expansion for the associated density of the time to ruin (see, e.g., Dickson and Willmot (2005)). In this thesis, we propose to analyze the long-standing finite-time ruin problem by incorporating the number of claims until ruin into the Gerber-Shiu analysis. As will be seen in Chapter 2, many nice analytic properties of the original Gerber-Shiu function are preserved by this generalized analytic tool. For instance, the Gerber-Shiu function still satisfies a defective renewal equation and can be generally expressed in terms of some roots of Lundberg's generalized equation in the Sparre Andersen risk model. In this thesis, we propose not only to unify previous methodologies on the study of the density of the time to ruin through the use of Lagrange's expansion theorem, but also to provide insight into the nature of the series expansion by identifying the probabilistic contribution of each term in the expansion through analysis involving the distribution of the number of claims until ruin. In Chapter 3, we study the joint generalized density of the time to ruin and the number of claims until ruin in the classical compound Poisson risk model. We also utilize an alternative approach to obtain the density of the time to ruin based on the Lagrange inversion technique introduced by Dickson and Willmot (2005). In Chapter 4, relying on the Lagrange expansion theorem for analytic inversion, the joint density of the time to ruin, the surplus immediately before ruin and the number of claims until ruin is examined in the Sparre Andersen risk model with exponential claim sizes and arbitrary interclaim times. To our knowledge, existing results on the finite-time ruin problem in the Sparre Andersen risk model typically involve an exponential assumption on either the interclaim times or the claim sizes (see, e.g., Borovkov and Dickson (2008)). Among the few exceptions, we mention Dickson and Li (2010, 2012) who analyzed the density of the time to ruin for Erlang-n interclaim times. In Chapter 5, we propose a significant breakthrough by utilizing the multivariate version of Lagrange's expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely when interclaim times are distributed as a combination of n exponentials. It is worth emphasizing that this technique can also be applied to other areas of applied probability. For instance, the proposed methodology can be used to obtain the distribution of some first passage times for particular stochastic processes. As an illustration, the duration of a busy period in a queueing risk model will be examined. Interestingly, the proposed technique can also be used to analyze some first passage times for the compound Poisson processes with diffusion. In Chapter 6, we propose an extension to Kendall's identity (see, e.g., Kendall (1957)) by further examining the distribution of the number of jumps before the first passage time. We show that the main result is particularly relevant to enhance our understanding of some problems of interest, such as the finite-time ruin probability of a dual compound Poisson risk model with diffusion and pricing barrier options issued on an insurer's stock price. Another closely related quantity of interest is the so-called occupation times of the surplus process below zero (also referred to as the duration of negative surplus, see, e.g., Egidio dos Reis (1993)) or in a certain interval (see, e.g., Kolkovska et al. (2005)). Occupation times have been widely used as a contingent characteristic to develop advanced derivatives in financial mathematics. In risk theory, it can be used as an important risk management tool to examine the overall health of an insurer's business. The main subject matter of Chapter 7 is to extend the analysis of occupation times to a class of renewal risk processes. We provide explicit expressions for the duration of negative surplus and the double-barrier occupation time in terms of their Laplace-Stieltjes transform. In the process, we revisit occupation times in the content of the classical compound Poisson risk model and examine some results proposed by Kolkovska et al. (2005). Finally, some concluding remarks and discussion of future research are made in Chapter 8.

Eskom is the major electricity supplier in South Africa and medium term forecasting within the company is a critical activity to ensure that enough electricity is generated to support the country's growth, that the networks can supply the electricity and that the revenue derived from electricity consumption is managed efficiently. This study investigates the most suitable forecasting technique for predicting monthly electricity consumption, one year ahead for four major municipalities within Kwa-Zulu Natal. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1997.

No abstract available. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1999.

No abstract available. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

Multilevel models account for different levels of aggregation that may be present in the data. Researchers are sometimes faced with the task of analysing data that are collected at different levels such that attributes about individual cases are provided as well as the attributes of groupings of these individual cases. Data with multilevel structure is common in the social sciences and other fields such as epidemiology. Ignoring hierarchies in data (where they exist) can have damaging consequences to subsequent statistical inference. This study applied multilevel models from frequentist and Bayesian perspectives to the Swaziland Demographic and Health Survey (SDHS) data. The first model fitted to the data was a Bayesian generalised linear mixed model (GLMM) using two estimation techniques: the Integrated Laplace Approximation (INLA) and Monte Carlo Markov Chain (MCMC) methods. The study aimed at identifying determinants of HIV in Swaziland and as well as comparing the different statistical models. The outcome variable of interest in this study is HIV status and it is binary, in all the models fitted the logit link was used. The results of the analysis showed that the INLA estimation approach is superior to the MCMC approach in Bayesian GLMMs in terms of computational speed. The INLA approach produced the results within seconds compared to the many minutes taken by the MCMC methods. There were minimal differences observed between the Bayesian multilevel model and the frequentist multilevel model. A notable difference observed between the Bayesian GLMMs and the the multilevel models is that of differing estimates for cluster effects. In the Bayesian GLMM, the estimates for the cluster effects are larger than the ones from the multilevel models. The inclusion of cluster level variables in the multilevel models reduced the unexplained group level variation. In an attempt to identify key drivers of HIV in Swaziland, this study found that age, age at first sex, marital status and the number of sexual partners one had in the last 12 months are associated with HIV serostatus. Weak between cluster variations were found in both men and women. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

Purpose: The purpose of this paper is to investigate whether there is a correlation between the actuarial assumptions, of listed groups in Large Cap on the Nasdaq Stockholm, equity ratio and their pensionplans funding status. Method: The study is based on a quantitative research method, where the analysis of annual reports takes place. The quantitative research method has enabled the paper to perform related analyzes and comparisons of means between groups, for listed companies equity ratio and pension obligation, and the relation to its actuarial assumptions. Correlation measurements are made using a non-parametric method, Spearman's rho, then further tested using one-sided hypotheses t-test. Theory: The backbone of the thesis is presented using two theories, earnings management and the principal-agent theory. These theories are intertwined with the previous researches, which also dealt with the essay topic of earnings management in previous years and in other countries. Empirical: Correlation analyzes between the studied actuarial assumptions and corporate groups solidity and pension financial status is presentedusing tables and charts. These are further analyzed using hypothesis tests and scatterplots. Conclusion: All tests resulted in very weak correlation between the different variables and can there for not be classified as significant. The conclusion that companies, listed in Large Cap on Nasdaq Stockholm, tend to make its actuarial assumptions in order to try to achieve a certain equity ratio, or to try to get their unfunded pension plans seem more funded than they actually are, is not possible to make.

By knowing the incidence of an infectious disease, we can ascertain the high risk factors of the disease as well as the e ectiveness of awareness programmes and treatment strategies. Since the work of Hugo Muench in 1934, many methods of estimating the force of infection have been developed, each with their own advantages and disadvantages. The objective of this thesis is to explore the di erent compartmental models of infectious diseases and establish and interpret the parameters associated with them. Seven models formulated to estimate the force of infection were discussed and applied to data obtained from CAPRISA. The data was agespeci c HIV prevalence data based on antenatal clinic attendees from the Vulindlela district in KwaZulu-Natal. The link between the survivor function, the prevalence and the force of infection was demonstrated and generalized linear model methodology was used i to estimate the force of infection. Parametric and nonparametric force of infection models were used to t the models to data from 2009 to 2010. The best tting model was determined and thereafter applied to data from 2002 to 2010. The occurring trends of HIV incidence and prevalence were then evaluated. It should be noted that the sample size for the year 2002 was considerably smaller than that of the following years. This resulted in slightly inaccurate estimates for the year 2002. Despite the general increase in HIV prevalence (from 54.07% in 2003 to 61.33% in 2010), the rate of new HIV infections was found to be decreasing. The results also showed that the age at which the force of infection peaked for each year increased from 16.5 years in 2003 to 18 years in 2010. Farrington's two parameter model for estimating the force of HIV infection was shown to be the most useful. The results obtained emphasised the importance of HIV awareness campaigns being targeted at the 15 to 19 year old age group. The results also suggest that using only prevalence as a measure of disease can be misleading and should rather be used in conjunction with incidence estimates to determine the success of intervention and control strategies. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

In many regions of the world, the solvency regulation of insurers is becoming more principle-based and market oriented. However, the exact forms of the solvency standards that are emerging in individual jurisdictions are not entirely consistent. A common risk and capital framework can level the global playing field and possibly reduce the cost of capital for insurers. In the thesis, a conceptual framework for measuring the insolvency risk of life insurance companies will be proposed. The two main advantages of the proposed solvency framework are that it addresses the issue of incentives in the calibration of the capital requirements and it also provides an associated decomposition of the insurer's insolvency risk by term. The proposed term structure of insolvency risk is an efficient risk summary that should be readily accessible to both regulators and policyholders. Given the inherent complexity of the long-term guarantees and options of typical life insurance policies, the term structure of insolvency risk is able to provide stakeholders with more complete information than that provided by a single number that relates to a specific period. The capital standards for life insurers that are currently existing or have been proposed in Canada, U.S., and in the EU are then reviewed within the risk and capital measurement framework of the proposed standard to identify potential shortcomings.