In this dissertation an overview on the real representation of quaternions in distribution theory is given. The density functions of the p-variate and matrix-variate quaternion normal distributions are derived from first principles, while that of the quaternion Wishart distribution is derived from the real associated Wishart distribution via the characteristic function. Applications of this theory in hypothesis testing is presented, and the density function of Wilks's statistic is derived for quaternion Wishart matrices. / Dissertation (MSc)--University of Pretoria, 2010. / Statistics / unrestricted

L'augmentation des concentrations de méthane dans l'atmosphère, directement imputable aux activités anthropiques, induit une accentuation de l'effet de serre et une dégradation de la qualité de l'air. Il existe encore à l'heure actuelle de grandes incertitudes concernant les estimations des émissions des dfférentes sources de méthane à l'échellelocale. Une meilleure caractérisation de ces sources permettrait de mettre en place des politiques d'adaptation et d'att énuation efficaces afin de réduire ces émissions. Nous avons développé une nouvelle méthode de quantificationdes émissions de méthane à l'échelle locale basée sur la combinaison de mesures atmosphériques mobiles et d'un modèle gaussien dans le cadre d'une inversion statistique. Les concentrations atmosphériques du méthane sont mesuréesainsi que celles d'un gaz traceur émis à un flux connu. Ces concentrations en gaz traceur sont utilisées pour sélectionnerla classe de stabilité représentant le mieux les conditions atmosphériques dans le modèle gaussien ainsi qu'à paramétrerl'erreur associée aux mesures et au modèle dans l'inversion statistique. Dans un premier temps, cette nouvelle méthoded'estimation des émissions de méthane a été testée grâce à des émissions contrôlées de traceur et de méthane dontles sources ont été positionnées suivant différentes configurations. J'ai ensuite appliqué cette méthode à deux sites réels connus pour leurs émissions de méthane, une exploitation agricole et une installation de distribution de gaz, afin de tester son applicabilité et sa robustesse dans des conditions plus complexes de répartition des sources de méthane. Cette méthode a permis d'obtenir des estimations des émissions totales des sites robustes prenant en compte la localisation du traceur par rapport aux sources de méthane. L'estimation séparéedes émissions des différentes sources d'un site s'est révélée fortement dépendante des conditions météorologiques durant les mesures. Je me suis ensuite focalisé sur les émissions de méthane associées au secteur des déchets en réalisant un certain nombre de campagnes de mesures au sein d'installations de stockagedes déchets non dangereux et de stations d'épuration. Les résultats obtenus pour ces différents sites montrent la grandevariabilité des émissions de méthane dans le secteur des déchets. / The increase of atmospheric methane concentrations since the beginning of the industrial era is directly linked to anthropogenic activities. This increase is partly responsible for the enhancement of the greenhouse effect leading to a rise of Earth's surface temperatures and a degradation of air quality. There are still considerable uncertainties regarding methane emissions estimates from many sources at local scale. A better characterization of these sources would help the implementation of effective adaptation and mitigation policies to reduce these emissions.To do so, we have developed a new method to quantify methane emissions from local sites based on the combination of mobile atmospheric measurements, a Gaussian model and a statistical inversion. These atmospheric measurements are carried out within the framework of the tracer method, which consists in emitting a gas co-located with the methane source at a known flow. An estimate of methane emissions can be given by measuring the tracer and methane concentrations through the emission plume coming from the site. This method presents some limitations especially when several sources and/or extended sources can be found on the studied site. In these conditions, the colocation of the tracer and methane sources is difficult. The Gaussian model enables to take into account this bad collocation. It also gives a separate estimate of each source of a site when the classical tracer release method only gives an estimate of its total emissions. The statistical inversion enables to take into account the uncertainties associated with the model and the measurements.The method is based on the use of the measured tracer gas concentrations to choose the stability class of the Gaussian model that best represents the atmospheric conditions during the measurements. These tracer data are also used to parameterize the error associated with the measurements and the model in the statistical inversion. We first tested this new method with controlled emissions of tracer and methane. The tracer and methane sources were positioned in different configurations in order to better understand the contributions of this method compared to the traditional tracer method. These tests have demonstrated that the statistical inversion parameterized by the tracer gas data gives better estimates of methane emissions when the tracer and methane sources are not perfectly collocated or when there are several sources of methane.In a second time, I applied this method to two sites known for their methane emissions, namely a farm and a gas distribution facility. These measurements enabled us to test the applicability and robustness of the method under more complex methane source distribution conditions and gave us better estimates of the total methane emissions of these sites that take into account the location of the tracer regarding methane sources. Separate estimates of every source within the site are highly dependent on the meteorological conditions during the measurements. The analysis of the correlations on the posterior uncertainties between the different sources gives a diagnostic of the separability of the sources.Finally I focused on methane emissions associated with the waste sector. To do so, I carried out several measurement campaigns in landfills and wastewater treatment plants and I also used data collected on this type of sites during other projects. I selected the most suitable method to estimate methane emissions of each site and the obtained estimates for each one of these sites show the variability of methane emissions in the waste sector.

The thesis proposes management options and risk minimizing in the field of building materials production technologies and related products using fuzzy logic and other risk management tools. The thesis indicates why some methodologies are not commonly used. The main purpose of this work (thesis) is to propose possible upgrades of standard methods in process capability and risk minimizing related to building materials and products. Markov analysis and fuzzy Markov chains are applied.

The goal of this master thesis is to make possible to perform system log analysis in more general way than well-known host-based instrusion detection systems (HIDS). The way how to achieve this goal is via proposed user-friendly regular expressions. This thesis deals with making regular expressions possible to use in the field of log analysis, and mainly by users unfamiliar with formal aspects of computer science.

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The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use. / Ph. D.

Taneichi(1993)提出一個新的適合度檢定統計量J²，具有近似卡方分配的性質。然而在小樣本的情形下，計算機模擬結果顯示，它的估計顯著水準大於期望顯著水準。所以本論文的重點之一，就是對J²進行改進，根據不同的準則，來選取一個適當的常數a。我們建議對每一觀測次數加一常數0.32，作為我們修正後的統計量，這個統計量我們記為J₁²。 　　另一探討的重點是在比較皮爾生卡方統計量X²，概似比例統計量G²，Cressie & Read統計量 I(2/3)，J²和J₁²之性質，我們想要了解在小樣本的情形之下，何者較接近於卡方分配，何者具有較強的檢定力。研究結果顯示，X²和I(2/3)較接近卡方分配，但J₁²又較G²及J²好；至於檢定力，我們發現沒有一個統計量在文中所探討的對立假設的情況下，同時都具有最大的檢定力。這些現象都可以用觀測次數對期望次數比值間的關係來解釋。 / Taneichi(1993) introduces a new goodness-of-fit statisticJ², which has an asymptotic chi-squared distribution. However, the results of simulation indicate that the levels of significance are in general bigger than the nominal levels, which prompts us to device a version of J² statistic which would perform better under small sample size situations. We suggest adding 0.32 to each observed value and find that the adjustment indeed works rearonably well. This version of J^2 statistic is denoted as J(1)^2. 　　Although Pearson chi-square statistic X², likelihood ratio statistic G², Cresse-Read statistic I(2/3), J^2 and J(1) ^2 all have asymptotic chi-squared distributions, their small sample behaviors are not expected to be the same. Comparisons based on simulation studies are then made. The conclusions are as follows : (1) In terms of levels of significance, X² and I(2/3) behave more like a chi-squared distribution. Though J(1) ^2 does not perform as good as X² and I(2/3), it does outperform G² and J². (2) In terms of powers, it does not seem that any of the test statistics has a clear advantage over the others.

In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications.

The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics)