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The detailed spatial and temporal influence of lightning on precipitation losses from the Earth's radiation belts is not yet well known. The precipitation is mainly due to the pitch angle scattering of electrons by lightning induced whistler mode waves. The World Wide Lightning Location Network (WWLLN) gives continuous real-time global lightning coverage with excellent time resolution. The detection effciency of WWLLN is unfortunately relatively low. This led to the normalisation of WWLLN with reference to Lightning Imaging Sensor (LIS)/Optical Transient Detector (OTD) data. LIS/OTD has very good detection effiency and spatial resolution. However, whereas WWLLN records strokes, LIS/OTD record flashes. Therefore the flash multiplicity had to be taken into account. The normalised WWLLN flash densities were compared to those of the South African Weather Service (SAWS) data, National Lightning Detection Network (NLDN) and the European LINET network. Then the average power per lightning flash was calculated to determine the energy flux incident on the ionosphere. Finally the WWLLN data was transformed to geomagnetic (MAG) coordinates using the Altitude Adapted Corrected Geomagnetic (AACGM) code. By applying absorption curves, the energy flux into the magnetosphere was estimated. These values were then compared to Trimpi produced Whistler-Induced Electron Precipitation (WEP) rates. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2012.

The main theme of this dissertation deals with the impact and consequences of non-normal distribution on the process capability index Cpm. In this thesis, much work has been done in this area including the properties of C^pm, the estimate of Cpm, under normality, its sensitivity to non-normality and also the relationship of Cpm to squared error loss. Related to Cpm is the unifying measure of process capability index Cpw. Several properties of C^pw are investigated. Much of the controversy surrounding the Cp index involves 6[sigma] in the denominator. It carries particular physical meaning when the process characteristic is normally distributed. A new index Cpo is proposed which is based on the difference between two order statistics. The sampling distribution of C^po is obtained for those cases where the process characteristic is uniform, exponential and normal distributions. The behavior of C^p, when n = 2, under non-normal situations such as uniform and exponential distributions is also investigated as a special case of C^po. Another major issue addressed in this dissertation is the Inverted Probability Loss Functions (IPLFs). It is a modified loss function found by inverting a probability density function which was first invented by my supervisor Dr. F.A. Spiring in 1993. The first loss function I studied is the inverted beta loss function (IBLF). I have found certain interesting properties that this class of loss function possesses such as the shape, the loss function and its associated risk function of the IBLF are scale invariant under linear transformation. Finally, I have investigated a few more IPLFs satisfying the usual loss function properties and developed some theorems in this portion of the study.

DNA profiles have become an extremely important tool in forensic investigations, and a match between a suspect and a crime scene specimen is highly incriminating. Presentation of this evidence in court, however, requires a statistical interpretation, one which reflects the uncertainty in the results due to measurement imprecision and sampling variability. No consensus has been reached about how to quantify this uncertainty, and the literature to date is lacking an objective review of possible methods. / This thesis provides a survey of approaches to statistical analysis of DNA profile data currently in use, as well as proposed methods which seem promising. A comparison of frequentist and Bayesian approaches is made, as well as a careful examination of the assumptions required for each method.

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