Electricity is one of the most stolen commodities in the world. Electricity theft can be defined as the criminal act of stealing electrical power. Several types of electricity theft exist, including illegal connections and bypassing and tampering with energy meters. The negative financial impacts, due to lost revenue, of electricity theft are far reaching and affect both developing and developed countries. . Here in South Africa, Eskom loses over R2 Billion annually due to electricity theft. Data mining and nonparametric statistical methods have been used to detect fraudulent usage of electricity by assessing abnormalities and abrupt changes in kilowatt hour (kWh) consumption patterns. Identifying effective measures to detect fraudulent electricity usage is an active area of research in the electrical domain. In this study, Support Vector Machines (SVM), Naïve Bayes (NB) and k-Nearest Neighbour (KNN) algorithms were used to design and propose an electricity fraud detection model. Using the Nelson Mandela Bay Municipality as a case study, three classifiers were built with SVM, NB and KNN algorithms. The performance of these classifiers were evaluated and compared.

Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure. Many tests have been developed over recent years to test the similarity of certain types of spatial data, such as spatial point patterns, geostatistical data and images. This research develops a similarity test able to handle various types of spatial data, for example images (modelled spatially), point patterns, marked point patterns, geostatistical data and lattice patterns. The test consists of three steps. The first step creates a pixel image representation of each spatial data set considered. In the second step a local similarity map is created from the two pixel image representations from step one. The local similarity map is obtained by either using the well-known similarity measure for images called the Structural SIMilarity Index (SSIM) when having continuous pixel values or a direct comparison in the case of discrete pixel values. The calculation of the final similarity measure is done in the third step of the test. This calculation is based on the S-index of Andresen's spatial point pattern test. The S-index is calculated as the proportion of similar spatial units in the domain where s_i is used as a binary indicator of similarity. In the case of discrete pixel values, s_i are still used as a binary input whereas in the case of continuous pixel values the resulting SSIM values are used as a non-binary s_i input. The proposed spatial similarity test is tested with a simulation study where the simulations are designed to have comparisons that are either 80% or 90% identical. With the simulation study it is concluded that the test is not sensitive to the resolution of the pixel image. The application is done on property valuations in Johannesburg and Cape Town. The test is applied to the similarity of property prices in the same area over different years as well as testing the similarity of property prices between the different areas of properties. / Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2020. / The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the author and are not necessarily to be attributed to the NRF. / Statistics / MSc (Advanced Data Analytics) / Unrestricted

In this mini-dissertation we discuss the spatial relationship between point processes and a linear network. As a starting point, we discuss basic spatial point processes and tests for first-order homogeneity. Following that, we discuss second-order properties of point processes in the form of Ripley's K-function for unmarked point patterns and the cross-K function for marked point patterns. We then get to the main focus of this mini-dissertation, that is, the spatial relationship between points and linear structures, particularly linear networks. Recently developed is a method to characterise the spatial relationship between points and linear networks by Comas et al. [13], similar to Ripley's K-function for point-to-point relationships. The non-stationarity of a linear network is of particular interest in how it affects the measurement of this spatial relationship, which has not been explicitly investigated in the literature before. To investigate this we consider the Poisson line process and how one might simulate a non-stationary line process. Furthermore, we discuss a mechanism to extend tests of first-order homogeneity of point patterns to line patterns. The non-stationary line process is used to model linear networks in the simulations conducted to determine the effect of this non-stationarity on the developed method, which was not covered in the original article [13]. The methodology is developed and tested on a real data set. / Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2020. / ESRI South Africa / Statistics / MSc (Advanced Data Analytics) / Unrestricted

Bibliography: pages 311-318. / In this study the distributional properties of certain multivariate complex quadratic forms and their characteristic roots are investigated. Multivariate complex distribution theory was originally introduced by Wooding (1956), Turin (1960) and Goodman (1963a) when they derived and studied the multivariate complex normal distribution. The multivariate complex normal distribution is the basis of complex distribution theory and plays an important role in various areas. In the area of multiple time-series the complex distribution theory is found very useful.

Includes bibliography. / This thesis describes methods of constructing models for cross-classified categorical data. In particular we discuss the construction of a class of approximating models and the selection of the most suitable model in the class. Examples of application are used to illustrate the methodology. The main purpose of the thesis is to demonstrate that it is both possible and advantageous to construct models which are specifically designed for the particular application under investigation. We believe that the methods described here allow the statistician to make good use of any expert knowledge which the client (typically a non-statistician) might possess on the subject to which the data relate.

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