A distribuição beta é apropriada para analisar dados de variáveis medidas no intervalo (0, 1), como taxas e proporções, como por exemplo a proporção de severidade de doenças em plantas. Portanto, dados que são pares observações de taxas e proporções, naturalmente pensa-se numa distribuição beta bivariada com suporte (0, 1)2. O objetivo deste trabalho constitui-se em encontrar a melhor distribuição beta bivariada na literatura para este caso e, além disso, tentar encontrar estimadores para seus parâmetros, a fim de verificar se esta distribuição escolhida se ajusta bem aos dados. Foi criada uma metodologia para a estimação dos parâmetros, utilizando aquela distribuição que consideramos a mais adequada. Posteriormente foram feitas simulações para avaliar a qualidade desses estimadores e, por fim, foram utilizados três bancos de dados com a finalidade de exemplificar esta metodologia. / Beta distribution is suitable for analyzing variable data measured in the range (0, 1), as rates and proportions, such as the proportion of disease severity in plants. Therefore, data that are paired observations rates and proportions naturally thinks in a bivariate distribution beta supported (0, 1)2. The objective of this work is on finding the best beta bivariate distribution in the literature for this case and, furthermore, try to find estimators for its parameters in order to verify that this chosen distribution fits the data well. A methodology was created for the estimation of parameters using that distribution we consider the most appropriate. Later simulations were performed to evaluate the quality of these estimators and, finally, we use three databases in order to illustrate this methodology.

Este trabalho apresenta uma análise estatística de contagens multivariadas proveniente de várias populações através de modelos de regressão. Foram considerados casos onde os vetores respostas obedeçam às distribuições Poisson multivariada e Poisson log-normal multivariada. Esta distribuição admite correlação de ambos sinais entre componentes do vetor resposta, enquanto que as distribuições mais usuais para dados de contagens (como a Poisson multivariada) admitem apenas correlação positiva entre as componentes do vetor resposta. São discutidos métodos de estimação e testes de hipóteses sobre os parâmetros do modelo para o caso bivariado. Estes modelos de regressão foram aplicados a um conjunto de dados referentes a contagens de dois tipos de defeitos em 100 gramas de fibras têxteis de quatro máquinas craqueadeiras, sendo duas de um fabricante e as outras de um segundo fabricante. Os resultados obtidos nos diferentes modelos de regressão foram comparados. Para estudar o comportamento das estimativas dos parâmetros de uma distribuição Poisson Log-Normal, amostras foram simuladas segundo esta distribuição. / Regression models are presented to analyse multivariate counts from many populations. Due to the random vector characteristic, we consider two classes of probability models: Multivariate Poisson distribution and Multivariate Poisson Log-Normal distribution. The last distribution admits negative and positive correlations between two components of a random vector under study, while other distributions (as Multivariate Poisson) admit only positive correlation. Estimation methods and test of hypothese on the parameters in bivariate case are discussed. The proposed techniques are illustrated by numerical examples, considering counts of two types of defects in 100g of textile fibers produced by four machines, two from one manufacturer and the other two from another one. The results from different regression models are compared. The empirical distribution of Poisson Log-Normal parameter estimations are studied by simulated samples.

As externalidades positivas ensejadas pela prestaÃÃo de serviÃos de saneamento bÃsico incluÃram a universalizaÃÃo do acesso aos serviÃos no marco regulatÃrio do setor. Nesse contexto, a ampliaÃÃo da oferta aparece como condiÃÃo necessÃria, mas nÃo suficiente para reduÃÃo no deficit desses serviÃos. Ao buscar responder ao problema investigativo deste trabalho - âquais fatores determinam a chance de o agente econÃmico residir num domÃcilio com determinada alternativa de saneamento?â - se pretende alcanÃar o objetivo da pesquisa: fornecer informaÃÃes para orientar polÃticas pÃblicas que propiciem o uso eficiente dos sistemas de saneamento. Foi empregado um modelo logit bivariado para testar as seguintes hipÃteses: existem mais atributos concorrentes aos serviÃos de saneamento para famÃlias com menor nÃvel de escolaridade; e iluminaÃÃo elÃtrica à um atributo concorrente ao serviÃo de esgotamento sanitÃrio pela rede geral. O modelo està apoiado na Teoria do Consumidor, cujo nÃvel de satisfaÃÃo aumenta ao residir num domicÃlio com maior nÃmero de atributos, e na Teoria dos PreÃos HedÃnicos, jà que os serviÃos de saneamento sÃo incorporados ao modelo como um entre vÃrios atributos disponÃveis no domicÃlio demandado pelo agente econÃmico. Os resultados apontam que a variÃvel exÃgena escolaridade à efetivamente relevante para explicar o acesso aos serviÃos de saneamento, especialmente por serviÃos de esgoto. Verifica-se, contudo, que resultados observados no contexto nacional podem nÃo refletir a realidade regional, de forma que algumas variÃveis representativas de modelos no plano nacional nÃo foram confirmadas no conceito local. / ABSTRACT The positive externalities occasioned by the basic sanitation, included the access to the service at the regulatory mark of the sector. In this context the supply enlargement turns up as a necessary condition, but not enough for a deficit reduction of these services. As we pursue to answer the investigative problem of this work - ? Which reasons determine the chance for the economic agent reside in a domicile with a determined alternative of sanitation? â It is intended to reach the research goal: provide information in order to orientate public policy which may propitiate the effective usage of the sanitation systems. A bivariate logit model was utilized to test the following hypothesis: there are more attributes concurring to the sanitation services for families with a lesser schooling; and electric illumination is a concurring attribute to the sewerage system through the general net. The model is supported on the Consumer Theory, whose satisfaction level increases as he resides in a domicile with a larger number of attributes and in the Theory of HedonicPrices, since the sanitation services are incorporated to the model as one among several available attributes in the domicile demanded by the economic agent. The results show that the exogenous variable schooling is effectively relevant to explain the access to sanitation services, especially those of sewerage. We verify, however that, the results observed in national context may not reflect the regional reality, so that some representative variables of models in national plan were not confirmed in local concept.

Neste trabalho propomos a representação de uma densidade bivariada segundo a natureza geométrica das marginais. Uma densidade contínua pode ser aproximada pela exponencial de um polinômio num domínio limitado. Tal aproximação permite estudar a influência do comportamento marginal e condicional sobre a densidade conjunta. Esse estudo é realizado encontrando os conjuntos dos possíveis valores dos coeficientes do polinômio segundo a informação dada sobre as densidades marginais ou as densidades condicionais. Também analisamos os coeficientes segundo algumas medidas de dependência. Concluímos mostrando a influência do comportamento marginal e condicional sobre variáveis aleatórias discretas. / In this work we propose a representation of a bivariate density according to the geometrical nature of the marginals. A continuous density can be approximated by the exponencial of a polynomial in a finite domain. Such approximation let us study the influence of the marginal and conditional behavior on the joint density. This study is done by finding the possible values of the polynomial coefficients upon the given information about the marginal or the conditional densities. We also analyze the coefficients according some dependence measures. We conclude showing the influence of the marginal and conditional behavior on discrete random variables.

This thesis consists of three studies which cover topics in the trading volume-market return volatility linkage, stock market return-aggregate mutual fund flow relationship as well as market return volatility-aggregate mutual fund flow interaction. Chapter 2 investigates the issue of volume-volatility linkage in the US market for the period 1990-2012 (S&P 500) and 1992-2012 (Dow Jones). We construct four sub-samples depending on three different structural points (the Asian Financial Crisis, the Dot-Com Bubble and the 2007 Financial Crisis). By employing univariate and bivariate GARCH processes, we find positive (negative) bidirectional linkages between these two aforementioned variables in various cases of the estimation, while a mixed one is observed in the remainder of these cases. Chapter 3 examines the issue of temporal ordering of the range-based stock market return (S&P 500 index) and aggregate mutual fund flow in the U.S. market for the period 1998-2012. We construct nine sub-samples represented by three fundamental cases of the whole data set. In addition, we take into consideration three essential indicators when splitting the whole data set, which are the 2000 Dot-Com Bubble, the 2007 Financial Crisis as well as the 2009 European Sovereign Debt Crisis. We examine the dynamics of the return-flow interaction by employing bivariate VAR model with various specifications of GARCH approach. Our principal findings display a bidirectional mixed feedback between stock market return and aggregate mutual fund flow for the majority of the sub-samples obtained. Nevertheless, we provide limited evidence of a positive bi-directional causality between return and flow. Chapter 4 investigates the dynamic relation between S&P 500 return volatility and U.S. aggregate mutual fund flow for the period spanning between 1998 and 2012. We assess the dynamics of the volatility-flow linkage by employing a bivariate VAR model with the GARCH approach which allows for long memory in the mean and the variance equations. In addition to the sub-samples obtained in chapter 3, we generate two measurements of volatility. Our baseline results indicate a variety of bidirectional mixed causalities between market return volatility and aggregate mutual fund flow in several sub-samples. In addition, we observe a negative/positive bi-directional relationship between volatility and flow in the rest of the sub-periods. Summarizing, a range of our findings are in line with the empirical underpinnings that most likely predict a significant linkage between the aforementioned variables. Finally, most of the bidirectional effects are found to be quite robust to the dynamics of the various GARCH processes employed in this thesis.

Many econometric analyses of commodity futures over the years have been performed using spot or front month contract prices. Using such daily prices without the consideration of the associated contract traded volumes is slightly erroneous because, in reality, traders will typically trade the ‘most liquid’ contract, that is, the contract with the largest average daily volume (ADV). The reason for this is in order to gain the best price when buying or selling. If this ‘true’ time series is to be considered, a mapping procedure is required to account for the price jumps at the time when a trader trades out of the expiring contract and enters the new front month contract. A key finding was that this effect was significant, irrespective of the size of the price jump, sometimes referred to as basis or roll and also due to the accumulated roll over a number of years corresponding to multiple contracts. It was also found that the mapping procedure has a significant effect on the time series and should hence always be employed if the realistic traded time series is to be considered. Given this phenomenon, algorithmically-traded commodities futures must necessarily employ such time series when creating metrics or considering an econometric analysis. The key findings include the importance of diversification in algorithmically-traded portfolios, utilising the AOM and PSI metrics. The mapping of data sets to create realistic ‘live-traded’ time series was found to be significant, while the optimal day of roll over prior to contract expiry was found to be related to the trading volumes for certain commodities. Other key findings include the causalities and spillovers within the metals sector where various relationships are evident once the results were processed and analysed, both pre and post mapping. Interestingly, the key relationships including bidirectional volatility and shock spillovers between the four key metals existed when the unmapped data was used however, many of the feedbacks within these relationships was lost when the mapped data sets were considered. A significant finding was therefore the consistent differences in findings between mapped and unmapped data sets attributed to the optimisation or favourability of the models (whether econometric or algorithmic). This is due to the unmapped data including roll or basis (which the models are fitted to) taking into account the roll or basis and utilising them in finding relationships between data sets. In the mapped data set (the time series seen by traders) the roll or basis is accounted for and hence the relationships found stand in real-time trading situations. The differences in the results show how the effect of mapping can be significant with unmapped data sets displaying results which will not exist in a real time traded time series.

There exists much controversy as to whether international migration in general, and migrant's remittances in particular, increase or decrease economic welfare at origin. Our research contributes to the international discussion on remittances by presenting novel insights on the basis of theoretical and empirical analysis. Analysis of remittances from macro-economic as well as micro-economic point of view reveals that remittances not only have growth enhancing effect but also have an equalizing impact on income distribution of the recipient economy. The first chapter shows how large flows of remittances not only help the receiver to accumulate necessary savings but also reduce the critical level of wealth needed to get access to the capital market to instigate entrepreneurship. The second chapter reveals that the measured impact of remittances on business investment have significant country heterogeneity; remittances facilitate entrepreneurship in those countries where the lenders of the capital market can predict smooth and increasing flow of remittances. The third chapter proposes that remittances work better than aid in enhancing growth of the recipient country and the reason is that remittances are more effective than aid in augmenting capital accumulation.

The Secondary Prevention in Uppsala Primary Health Care Project (SUPRIM) is a randomized controlled trial evaluating the effects of cognitive behavioral therapy on coronary heart disease patients. Various outcomes of psychological and physical health are recorded every six months approximately, over the course of two years after entry to the trial. In this thesis, relationships between the psychological outcome variables, Stress, Anxiety, Depression and Exhaustion, and five physical health biomarkers, are assessed using bivariate linear mixed models. Significant associations are found between one of the biomarkers and both Depression and Exhaustion, and also between one of the other biomarkers and Exhaustion.

Having just survived what is arguably the worst financial crisis in time, it is expected that the focus on regulatory capital held by financial institutions such as banks will increase significantly over the next few years. The probability of default is an important determinant of the amount of regulatory capital to be held, and the accurate calibration of this measure is vital. The purpose of this study is to propose the use of the Shannon entropy when determining the parameters of the prior bivariate beta distribution as part of a Bayesian calibration methodology. Various bivariate beta distributions will be considered as priors to the multinomial distribution associated with rating categories, and the appropriateness of these bivariate beta distributions will be tested on default data. The formulae derived for the Bayesian estimation of Shannon entropy will be used to measure the certainty obtained when selecting the prior parameters. / Dissertation (MSc)--University of Pretoria, 2010. / Statistics / unrestricted

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.