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The increasing usage of algorithms and extensive collections of data have changed the discipline of finance and created new possibilities for analyzing the financial markets. To further explore the potential of developing new methods for understanding financial market behaviour, this thesis examines the first digit probability distribution of Benford's Law and its applicability within the financial markets. The research investigates various indices', equities', and technical analysis tools' conformity to Benford's Law by using relative price changes and volume traded. It was found that both indices and equities exhibit resemblance with Benford's Law, whereas technical analysis tools did not. In addition, the relevance of data frequency was explored, but it was deemed not to have any effect on conformity found. In an attempt to apply the findings, a regression analysis was conducted to forecast volatility. However, even though correlation was found, the regression model failed to predict future volatility accurately. / Den ökade användningen av algoritmer och omfattande datainsamling har förändrat det finansiella spelrummet och skapat nya möjligheter för analys av finansmarknaden. För att ytterligare undersöka potentialen i att utveckla nya metoder för att förstå finansmarknadens beteende utforskar denna avhandling Benfords lag och dess tillämpbarhet på den finansiella marknaden. Studien testar olika index, aktiers och tekniska analysverktygs överensstämmelse med Benfords lag genom att använda relativa prisförändringar och handlad volym. Det visade sig att både index och aktier följer Benfords lag medan tekniska analysverktyg inte gjorde det. Dessutom undersöktes datafrekvensens relevans, men detta ansågs inte ha någon effekt på överensstämmelsen med fördelningen. I ett försök att tillämpa resultaten genomfördes en regressionsanalys för att prognosticera volatilitet. Korrelation hittades men regressionsmodellen gav inte ett tillförlitligt resultat.

Orientador: Selene Maria Coelho Loibel / Resumo: Esta dissertação tem como foco a análise de dados categóricos, uma parte integrante da Análise Multivariada que interpreta a informação que está contida em dados discretos provenientes de contagens de eventos, possuindo características de nidas pela combinação das categorias de duas ou mais variáveis. A análise de dados categóricos é de grande importância dentro da Estatística pois tem aplicabilidade em variadas áreas do conhecimento. Os dados utilizados, foram coletados através de um question ário aplicado aos alunos de cinco Escolas Técnicas Estaduais (Etec) que nalizaram os cursos técnicos em 2018 e 2019. A pesquisa teve como objetivo obter dados locais e analisar se os alunos pretendem trabalhar ou continuar estudando na mesma área do curso que estão concluindo, se os alunos estão satisfeitos com os cursos que estão fazendo, se pretendem voltar para Etec e fazer outro curso complementar, entre outros questionamentos. Devido à natureza dos dados obtidos, as técnicas de análise de dados categóricos são adequadas e devem ser aplicadas para modelar e fazer inferências sobre os aspectos de interesse. Esta análise pode levar a resultados que serão de grande utilidade para essas Etecs. / Abstract: This dissertation focuses on the Categorical Data Analysis, an integral part of the Multivariate Analysis, which interprets embedded information in discrete data resulting from event counts, having characteristics de ned by combinations of categories from two or more variables. The categorical data analysis is of considerable importance within Statistics since it has a wide applicability in several areas of knowledge. The data set used was collected through a questionnaire applied to students from ve Public Technical Schools (Etec) that nished the technical courses in 2018 and 2019. The research aims to gather local data and analyze whether students intend to work or continue studying in the same eld of the technical course they are completing, whether students are satis ed with the courses they are attending, whether they want to go back to Etec and take another complementary course, among other questions. Due to the nature of the data obtained, categorized data analysis techniques are adequate and should be applied to model and make inferences about the aspects of interest. This analysis can be leaded to outcomes that will be very useful to these Etecs. / Mestre

The main purpose of this thesis is to consider usual statistical tests for discrete data and to present some recent developments around them. Contents can be divided into three parts. In the first part we consider the general issue of misclassification and its impact on usual test results. A suggested diagnostic examination of the misclassification process leads to simple and direct investigation tools to determine whether conclusions are very sensitive to classification errors. An additional probabilistic approach is presented, in order to refine the discussion in terms of the risk of getting contradictory conclusions whenever misclassified data occur. In the second part we propose a general approach to deal with the issue of multiple sub-testing procedures. In particular, when the null hypothesis is rejected, we show that usual re-applications of the test to selected parts of the data can provide non-consistency problems. The method we discuss is based on the concept of decisive subsets, set as the smallest number of categories being sufficient to reject the null hypothesis, whatever the counts of the remaining categories. In this framework, we present an iterative step-by-step detection process based on successive interval building and category count comparison. Several examples highlight the gain our method can bring with respect to classical approaches. The third and last part is consecrated to the framework of item response theory, a field of psychometrics. After a short introduction to that topic, we propose first two enhanced iterative estimators of proficiency. Several theoretical properties and simulation results indicate that these methods ameliorate the usual Bayesian estimators in terms of bias, among others. Furthermore, we propose to study the link between response pattern misfit and subject's variability (the latter as individual latent trait). More precisely, we present "maximum likelihood"-based joint estimators of subject's parameters (ability and variability); several simulations suggest that enhanced estimators also have major gain (with respect to classical ones), mainly in terms of estimator's bias.

Current status data are usually obtained with a failure time variable T which is diffcult observed but can be determined to lie below or above a random monitoring time or inspection time t. In this work we consider bivariate current status data ${t,delta_1,delta_2}$ and assume we have some prior information of the bivariate failure time variables T1 and T2. Our main goal is to find an optimal inspection time for testing the relationship between T1 and T2.

In some applications, explicit codes are provided for missing data such as NA (not available) however many applications do not provide such explicit codes and valid or invalid data codes are recorded as legitimate data values. Such missing values are known as disguised missing data. Disguised missing data may affect the quality of data analysis negatively, for example the results of discovered association rules in KDD-Cup-98 data sets have clearly shown the need of applying data quality management prior to analysis. In this thesis, to tackle the problem of disguised missing data, we analyzed embedded unbiased sample heuristic (EUSH), demonstrated the methods drawbacks and proposed a new methodology based on Chi Square Two Sample Test. The proposed method does not require any domain background knowledge and compares favorably with EUSH.

Based on the load survey study, a stratified sampling method is proposed to select the proper size of customers so that the load patterns derived can represent the load behavior of whole customer population. In this study there are 1315 customers out of Taipower customers over various service classes are selected for the installation of intelligent meters in the field to measure the power consumption within every 15 minutes. The bad data detection is performed to identify the abnormal power consumption by executing the Chi-square test. The standardized daily load pattern of each customer class has been derived with the mean per-unit method of customer load. The billing data are retrieved from the customer information system and applied to derive the customer daily load pattern by considering the customer load patterns. According to the total power consumption by all customers within the same class and considering the corresponding daily load pattern, the daily load profile of the customer class is then determined. By aggregating the load profiles of all customer classes, the daily load composition and load model of each service district can therefore be solved. By the same manner, the daily load pattern of whole Taipower system can be derived and it can be used to support the proper design of tariff structure according to the respective contribution of system power demand by each customer class. To investigate the overloading of distribution main transformers during the summer season, the correlations analysis of customer power consumption and temperature is performed. The effect of temperature change to the power consumption of each customer class is solved by multiple regression analysis with 95% confidential level. Based on the temperature sensitivity and the corresponding load composition, the load change due to temperature rise for various customer classes can be estimated. To demonstrate the impact of temperature change to distribution system operation, considering the temperature sensitivity of power consumption and load composition solves the power demand at each load bus. By updating the bus load demand due to temperature change, the feeder loading and power loss is therefore derived. To resolve the over loading problem of distribution feeders and main transformers during the summer season, a temperature adaptive switching operation has been proposed to perform the proper load transfer among the feeders/main transformers. In this dissertation, the effect of temperature change to the time varying characteristics of load buses and power transmission in Taipower is investigated. The dc circuit model of Taipower system and the temperature effect of customer power consumption are considered in the stochastic load flow analysis. With the temperature rise, the power demand of northern buses is increased dramatically and more power has to be transmitted from the southern region. The large voltage angle difference is significantly various between system buses during the summer peak period. It is suggested that the safety margin assessment of system operation has to be executed by considering the temperature effect to the bus loading of power systems.

This thesis presents several statistical analysis on a cooperative project with Dr. Pallas and Yuting Mao from Biology Department of Georgia State University. This research concludes the impact of cauterize size of animals’ midbrain on auditory and visual response in brains. Besides some already commonly used statistical analysis method, such as MANOVA and Frequency Test, a unique combination of Permutation Test, Kolmogorov-Smirnov Test and Wilcoxon Rank Sum Test is applied to our non-parametric data. Some simulation results show the Permutation Test we used has very good powers, and fits the need for this study. The result confirms part of the Biology Department’s hypothesis statistically and enhances more complete understanding of the experiments and the potential impact of helping patients with Acquired Brain Injury.

In this dissertation we developed theoretical models to analyse Gaussian and multinomial distributions. The analysis is focused on classification in high dimensional feature spaces and provides a basis for dealing with issues such as data sparsity and feature selection (for Gaussian and multinomial distributions, two frequently used models for high dimensional applications). A Naïve Bayesian philosophy is followed to deal with issues associated with the curse of dimensionality. The core treatment on Gaussian and multinomial models consists of finding analytical expressions for classification error performances. Exact analytical expressions were found for calculating error rates of binary class systems with Gaussian features of arbitrary dimensionality and using any type of quadratic decision boundary (except for degenerate paraboloidal boundaries). Similarly, computationally inexpensive (and approximate) analytical error rate expressions were derived for classifiers with multinomial models. Additional issues with regards to the curse of dimensionality that are specific to multinomial models (feature sparsity) were dealt with and tested on a text-based language identification problem for all eleven official languages of South Africa. / Thesis (M.Ing. (Computer Engineering))--North-West University, Potchefstroom Campus, 2009.

Despite the huge national energy resources, many Nigerians do not have access to high quality, modern energy services. For those with access, energy supply lacks reliability, especially in the case of liquefied petroleum gas (LPG). Hence this research considers the possibility of enhancing the household use of LPG. It analyzes the factors affecting the current demand and supply. Salient features of the LPG supply and distribution system were also discussed. On the basis of the existing situation, barriers of increasing LPG use, in particular, the problems regarding affordability, priCing, government poliCies, safety, transportation and distribution were analyzed and identified statistically using the chi-square statistical method as a tool. Finally, on the basis of the challenges identified, suggestions and recommendations were made regarding the policies through which the problems could be overcome. Furthermore, a model was developed and tested for an effective marketing strategy of LPG in Warri Nigeria. ii / Thesis (M.Ing. (Development and Management Engineering))--North-West University, Potchefstroom Campus, 2009.