Thesis (Ph. D.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 119-134).

Thesis (M.A.S.)--Memorial University of Newfoundland, 2003. / Bibliography: leaves 48-50. Also available online.

Thesis (Ph.D.) - University of Queensland, 2005. / Includes bibliography.

Investors and financial analysts spend an inordinate amount of time, resources and effort in an attempt to perfect the science of maximising the level of financial returns. To this end, the field of distribution modelling and analysis of firm size effect is important as an investment analysis and appraisal tool. Numerous studies have been conducted to determine which distribution best fits stock returns (Mandelbrot, 1963; Fama, 1965 and Akgiray and Booth, 1988). Analysis and review of earlier research has revealed that researchers claim that the returns follow a normal distribution. However, the findings have not been without their own limitations in terms of the empirical results in that many also say that the research done does not account for the fat tails and skewness of the data. Some research studies dealing with the anomaly of firm size effect have led to the conclusion that smaller firms tend to command higher returns relative to their larger counterparts with a similar risk profile (Banz, 1981). Recently, Janse van Rensburg et al. (2009a) conducted a study in which both non- normality of stock returns and firm size effect were addressed simultaneously. They used a scale mixture of two normal distributions to compare the stock returns of large capitalisation and small capitalisation shares portfolios. The study concluded that in periods of high volatility, the small capitalisation portfolio is far more risky than the large capitalisation portfolio. In periods of low volatility they are equally risky. Janse van Rensburg et al. (2009a) identified a number of limitations to the study. These included data problems, survivorship bias, exclusion of dividends, and the use of standard statistical tests in the presence of non-normality. They concluded that it was difficult to generalise findings because of the use of only two (limited) portfolios. In the extension of the research, Janse van Rensburg (2009b) concluded that a scale mixture of two normal distributions provided a more superior fit than any other mixture. The scope of this research is an extension of the work by Janse van Rensburg et al. (2009a) and Janse van Rensburg (2009b), with a view to addressing several of the limitations and findings of the earlier studies. The Janse van rensburg (2009b) study was based on data from the Johannesburg Stock Exchange (JSE); this study seeks to compare their research by looking at the New York Stock Exchange (NYSE) to determine if similar results occur in developed markets. For analysis purposes, this study used the statistical software package R (R Development Core Team 2008) and its package mixtools (Young, Benaglia, Chauveau, Elmore, Hettmansperg, Hunter, Thomas, Xuan 2008). Some computation was also done using Microsoft Excel. This dissertation is arranged as follows: Chapter 2 is a literature review of some of the baseline studies and research that supports the conclusion that earlier research finding had serious limitations. Chapter 3 describes the data used in the study and gives a breakdown of portfolio formation and the methodology used in the study. Chapter 4 provides the statistical background of the methods used in this study. Chapter 5 presents the statistical analysis and distribution fitting of the data. Finally, Chapter 6 gives conclusions drawn from the results obtained in the analysis of data as well as recommendations for future work.

Neste trabalho, alguns resultados, tais como, função geradora de momentos, relações de recorrência para os momentos e alguns teoremas da classe de distribuições em séries de potencias modificadas (MPSD) proposta por Gupta (1974) e da classe de distribuições em séries de potências modificadas inflacionadas (IMPSD) tanto em um ponto diferente de zero como no ponto zero são apresentados. Uma aplicação do Modelo Poisson padrão, do modelo binomial negativo padrão e dos modelos inflacionados de zeros para dados de contagem, ZIP e ZINB, utilizando-se as técnicas dos MLGs, foi realizada para dois conjuntos de dados reais juntamente com o gráfico normal de probabilidade com envelopes simulados. Também foi proposta a distribuição Weibull binomial negativa (WNB) que é bastante flexível em análise de dados positivos e foram estudadas algumas de suas propriedades matemáticas. Esta é uma importante alternativa para os modelos Weibull e Weibull geométrica, sub-modelos da WNB. A demostração de que a densidade da distribuição Weibull binomial negativa pode ser expressa como uma mistura de densidades Weibull é apresentada. Fornecem-se, também, seus momentos, função geradora de momentos, gráficos da assimetria e curtose, expressoes expl´citas para os desvios médios, curvas de Bonferroni e Lorenz, função quantílica, confiabilidade e entropia, a densidade da estat´stica de ordem e expressões explícita para os momentos da estatística de ordem. O método de máxima verossimilhança é usado para estimar os parametros do modelo. A matriz de informação esperada ´e derivada. A utilidade da distribuição WNB está ilustrada na an´alise de dois conjuntos de dados reais. / In this paper, some result such as moments generating function, recurrence relations for moments and some theorems of the class of modified power series distributions (MPSD) proposed by Gupta (1974) and of the class of inflated modified power series distributions (IMPSD) both at a different point of zero as the zero point are presented. The standard Poisson model, the standard negative binomial model and zero inflated models for count data, ZIP and ZINB, using the techniques of the GLMs, were used to analyse two real data sets together with the normal plot with simulated envelopes. The new distribution Weibull negative binomial (WNB) was proposed. Some mathematical properties of the WNB distribution which is quite flexible in analyzing positive data were studied. It is an important alternative model to the Weibull, and Weibull geometric distributions as they are sub-models of WNB. We demonstrate that the WNB density can be expressed as a mixture of Weibull densities. We provide their moments, moment generating function, plots of the skewness and kurtosis, explicit expressions for the mean deviations, Bonferroni and Lorenz curves, quantile function, reliability and entropy, the density of order statistics and explicit expressions for the moments of order statistics. The method of maximum likelihood is used for estimating the model parameters. The expected information matrix is derived. The usefulness of the new distribution is illustrated in two analysis of real data sets.

Neste trabalho apresenta-se duas novas distribuições de probabilidade obtidas de dois métodos de generalização da distribuição log-logística com dois parâmetros (LL(?,?)). O primeiro método descrito em Marshall e Olkin (1997) transforma a nova distribuição, agora com três parâmetros e denominada distribuição log-logística modificada (LLM (v,?,?)), mais flexível porém, não muda a forma geral da função de taxa de falha e o novo parâmetro v, não influência no cálculo da assimetria e curtose. O segundo método utiliza a classe de distribuições Kumaraswamy proposta por Cordeiro e Castro (2010), para construir a nova distribuição de probabilidade, denominada distribuição Kumaraswamy log-logística (Kw-LL(a,b,?,?)), a qual considera dois novos parâmetros a e b obtendo ganho nas formas da função de taxa de falha, que agora além de modelar dados onde a função de taxa de falha tem forma decrescente e unimodal, modela forma crescente e forma de U. Também foi proposto as distribuições logística modificada (LM (v,µ,?)) e Kumaraswamy logística (Kw-L (a,b, µ,?)$) para a variável Y=log(T), em que T ~ LLM (v,?,?) no caso da distribuição logística modificada e T ~ Kw-LL(a,b,?,?) no caso da distribuição Kw-L. Com reparametrização ? = exp(µ) e ? = 1/?. Da mesma forma que a distribuição LLM, não há ganho quanto a forma da função de taxa de falha da distribuição logística modificada e o parâmetro v não contribuiu para o cálculo da assimetria e curtose desta distribuição. O modelo de regressão locação e escala foi proposto para ambas as distribuições. Por fim, utilizou-se dois conjuntos de dados, para exemplificar o ganho das novas distribuições Kw-LL e Kw-L em relação as distribuições log-logística e logística. O primeiro conjunto refere-se a dados de tempo até a soro-reversão de 143 crianças expostas ao HIV por via vertical, nascidas no Hospital das Clínicas da Faculdade de Medicina de Ribeirão Preto no período de 1995 a 2001, onde as mães não foram tratadas. O segundo conjunto de dados refere-se ao tempo até a falha de um tipo de isolante elétrico fluido submetivo a sete níveis de voltagem constante. / In this work, are presented two new probability distributions, obtained from two generalization methods of the log-logistic distribution, with two parameters (LL (?, ?)). The first method described in Marshall e Olkin (1997) turns the new distribution, now with three parameters, called modified log-logistic distribution (LLM(v, ?, ?)). This distribution is more flexible, but, does not change the general shape of the failure rate function, as well as the new parameter v, does not influence the calculus of skewness and kurtosis. The second method, uses the class of distributions Kumaraswamy proposed by Cordeiro and Castro (2010). To build the new probability distribution, called Kumaraswamy log-logistic distribution (Kw-LL(a,b,?,?)), which considers two new parameters a and b gaining in the forms of failure rate function, that now, even modeling data where the failure rate function has decreasing and unimodal shape, models the increasing form and the U-shaped. Also, were proposed the distributions modified logistic (LM (v,µ,?)) and Kumaraswamy logistics (Kw-L (a,b,µ,?)) for the variable Y=log(T), where T ~ LLM(v,?,?) in the case of the modified logistic distribution and T ~ Kw-LL (a,b,?,?) in the case of Kw-L distribution, with reparametrization ? =exp(µ) and ? = 1/?. As in the distribution LLM, there is no gain for the shape of the failure rate function of modified logistic distribution and the parameter v does not contribute to the calculation of skewness and kurtosis of the distribution. The location and scale regression models were proposed for both distributions. As illustration, were used two datasets to exemplify the gain of the new distributions Kw-LL and Kw-L compared with the log-logistic and logistic distributions. The first dataset refers to the data of time until soro-reversion of 143 children exposed to HIV through vertical, born in the Hospital of the Medical School of Ribeirão Preto during the period 1995 to 2001, where mothers were not treated. The second dataset refers to the time until the failure of a type of electrical insulating fluid subjected to seven constant voltage levels

Recentemente, Cordeiro e de Castro (2011) apresentaram uma classe generalizada baseada na distribuição Kumaraswamy (Kw-G). Essa classe de distribuições modela as formas de risco crescente, decrescente, unimodal e forma de U ou de banheira. Uma importante distribuição pertencente a essa classe é a distribuição Kumaraswamy Weibull modificada (KwMW) proposta por Cordeiro; Ortega e Silva (2013). Com isso foi utilizada essa distribuição para o desenvolvimento de algumas novas propriedades e análise bayesiana. Além disso, foi desenvolvida uma nova distribuição de probabilidade a partir da distribuição gama generalizada geométrica (GGG) que foi denominada de gama generalizada geométrica exponenciada (GGGE). Para a nova distribuição GGGE foram calculados os momentos, a função geradora de momentos, os desvios médios, a confiabilidade e as estatísticas de ordem. Desenvolveu-se o modelo de regressão log-gama generalizada geométrica exponenciada. Para a estimação dos parâmetros, foram utilizados os métodos de máxima verossimilhança e bayesiano e, finalmente, para ilustrar a aplicação da nova distribuição foi analisado um conjunto de dados reais. / Recently, Cordeiro and de Castro (2011) showed a generalized class based on the Kumaraswamy distribution (Kw-G). This class of models has crescent risk forms, decrescent, unimodal and U or bathtub form. An important distribution belonging to this class the Kumaraswamy modified Weibull distribution (KwMW), proposed by Cordeiro; Ortega e Silva (2013). Thus this distribution was used to develop some new properties and bayesian analysis. Furthermore, we develop a new probability distribution from the generalized gamma geometric distribution (GGG) which it is called generalized gamma geometric exponentiated (GGGE) distribution. For the new distribution we calculate the moments, moment generating function, mean deviation, reliability and order statistics. We define a log-generalized gamma geometric exponentiated regression model. The methods used to estimate the model parameters are: maximum likelihood and bayesian. Finally, we illustrate the potentiality of the new distribution by means of an application to a real data set.

Zhang Chongqi. / "November 2001." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 127-141). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Leung Shek-hay. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 53-55). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Finite Mixtures of Structural Equation Model --- p.4 / Chapter Chapter 3 --- Bayesian Approach --- p.7 / Chapter Chapter 4 --- Two-stage Approach --- p.16 / Chapter Chapter 5 --- Simualtion Study --- p.22 / Chapter 5.1 --- Performance of the Two Approaches --- p.22 / Chapter 5.2 --- Influence of Prior Information of the Two Approaches --- p.26 / Chapter 5.3 --- Influence of the Component Probability to the Two Approaches --- p.28 / Chapter 5.4 --- Performance of the Two Approaches when the Components are not well-separated --- p.29 / Chapter Chapter 6 --- A Real Data Analysis --- p.31 / Chapter Chapter 7 --- Conclusion and Discussion --- p.35 / Appendix A Derviation of the Conditional Distribution --- p.37 / Appendix B Manifest Variables in the ICPSR Example --- p.39 / Appendix C A Sample LISREL Program for a Classified Group in the Simualtion Study --- p.40 / Appendix D A Sample LISREL Program for a Classified Group in the ICPSR Example --- p.41 / Tables 1-9 --- p.42 / Figures 1-2 --- p.51 / References --- p.53