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A research report submitted in partial fulfilment of Mathematical Statistics Masters by Coursework and Research Report to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2019 / The growing demand for generic drugs has led to an increase in the generic drug industry. As a result, there has been a growing demand for bioequivalence studies. The challenges with the bioequivalence studies arose with the method used to quantify bioavailability. Bioavailability is commonly estimated by the area under the concentration-time curve (AUC), which is traditionally estimated by Non-Compartmental Analysis (NCA) such as interpolation in aid of the trapezoidal rule. However, when the number of samples per subject is insufficient, the NCA estimates may be biased and this can result in incorrect conclusions about bioequivalence. Alternatively, AUC can be estimated by the Non-Linear Mixed Effect Model (NLMEM). The objective of this study is to evaluate bioequivalence on lnAUC estimated by using a NCA approach to those based on the lnAUC estimated by the NLMEM approach. The NCA and NLMEM approaches are compared on the resulting bias when the linear mixed effect model is used to analyse the lnAUC data estimated by each method. The methods are evaluated on simulated and real data. The 2x2 crossover designs of different sample sizes and sampling time intensities are simulated using two null hypotheses. In each crossover design, concentration profiles are simulated with different levels of between-subject variability, within-subject variability and residual error variance. A higher bias is obtained with the lnAUC estimated by the NCA approach for trials with a limited number of samples per subject. The NCA estimates provide satisfactory global TypeI-error results. The NLMEM fails to distinguish between the existing formulation differences when the residual variability is high. / TL (2020)

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In this dissertation, the synthesis of system reliability from the reliabilities of the componentry constituting the system is considered. For the purpose of contextual elucidation, major emphasis is accorded to complex missile systems. / Ph. D.

This paper is concerned with the statistical approach to population genetics. The genetical characteristics of the population under consideration are the population size and the gene frequencies. The limitations on the population are (a) the individuals are either all haploids or all diploids; (b) the alleles are only two in number, either A or a; (c) there are no selection and migration pressures occurring in the population. Three main model types, the branching processes, the Markov chains, and the diffusion processes are discussed. Published results on the subject are presented along with some new investigations. Comparable results obtained by various authors are checked, some of which are found to be invalid. Continuous approximations are used to derive some of the results of discrete processes, but a chapter is devoted to the justification of such approximations. / M.S.

In this thesis, a stochastic model was utilized to predict the water content and sediment deposition characteristics in the Mazar Reservoir in Ecuador. The results obtained were compared with those reported in the project's feasibility study. The methodology used in this study was based on the assumption that annual water inflow can be taken as a random variable and annual water contents in the reservoir form an independent series of first-order, homogeneous Markov Chains. The available stream flow records indicated that normal and log-normal probability distributions would adequately characterize the annual water inflows. Using Moran's storage theory, expected values of the reservoir water contents were calculated for consecutive years until the storage probability transition matrix operation yielded a stationary condition. Annual amounts of sediment deposition in the reservoir were determined as the difference between annual sediment inflows and outflows. Two different scenarios were applied to calculate the annual sediment inflows. In the first scenario, based on the deterministic sediment rating equations, the resulting sediment rates were assigned the same probabilities as the water inflows. In the second scenario, the annual sediment rates were also considered as random variables normally distributed around the mean values. The results obtained indicated that a stochastic model, such as the one employed in this study, can be effectively used to predict sediment deposition in a reservoir to complement the predictions obtained with deterministic methods, and can even yield a more reliable spectrum of results that can be associated with various confidence levels, particularly when the data on actual sediment measurements is scarce. / M.S.