A distribuição gama generalizada (GG) possui, como casos particulares, distribuição Weibull, log-normal, gama, qui-quadrado, entre outras. Por essa razão, ela e considerada uma distribuição exvel no ajuste dos dados. A ideia de Cordeiro e Castro (2011) foi utilizada para o desenvolvimento de duas novas distribuições de probabilidade a partir da distribuição GG. Uma delas e denominada de Kumaraswamy gama generalizada (KumGG) e possui cinco parâmetros; a outra distribuição e uma modificação de um dos parmetros de forma da distribuição KumGG e foi denominada de distribuição Kumaraswamy gama generalizada estendida (KumGGE). Desenvolveu-se o modelo de regressão log-Kumaraswamy gama generalizada estendida. Alem disso, a ideia de Adamidis e Loukas (1998) para modicar distribuições foi utilizada para a distribuição GG; essa nova distribuição foi nomeada de gama generalizada geometrica (GGG). A vantagem desses novos modelos reside na capacidade de acomodar varias formas da função risco eles tambem se mostraram uteis na discriminação de modelos. Para cada um dos modelos foram calculados os momentos, função geradora de momentos, os desvios medios, a conabilidade e a função densidade de probabilidade da estatistica de ordem. Para a estimação dos parâmetros, foram utilizados os metodos de maxima verossimilhanca e bayesiano e, finalmente, para ilustrar a aplicação das novas distribuições foram analisados alguns conjuntos de dados reais. / The generalized gamma (GG) distribution has as particular cases the Weibull, log-normal, gamma and Chi-square distributions, among others. For this reason, it is considered a exible distribution for tting data. In this paper, the idea of Cordeiro and Castro (2011) is used to develop two new probability distributions based on the GG distribution. The rst is called the generalized gamma Kumaraswamy (KumGG) and has ve parameters, while the other involves a modication of one of the shape parameters of the KumGG distribution and is called the extended generalized gamma Kumaraswamy (KumGGE). Based in these, we develop the extended generalized log-Kumaraswamy regression model. Besides this, we employ the idea regarding modifying distributions of Adamidis and Loukas (1998) for the GG distribution, calling this new distribution the geometric generalized gamma (GGG). The advantage of these new models rests in their capacity to accommodate various risk function forms. They are also useful in model discrimination. We calculate the moments, moments generating function, mean deviations, reliability and probability density function of the order statistics. To estimate the parameters we use the maximum likelihood and Bayesian methods. Finally, to illustrate the application of the new distributions, we analyze some real data sets.

O milho é uma das culturas mais importantes do mundo, pois os produtos dele oriundos são largamente utilizados na indústria de amidos, na alimentação animal e humana, e também na produção de energia proveniente de biomassa. Por esse motivo, há sempre um grande interesse em conhecer a potencialidade de uso dos principais materiais genéticos disponíveis em relação aos ambientes em que serão inseridos. Este trabalho teve como objetivo central caracterizar, para o genótipo DKB-390 conduzido sob condição irrigada, atributos ecofisiológicos como área foliar, eficiência de uso da radiação, coeficiente de extinção, coeficientes de cultura, consumo hídrico e componentes de espiga; bem como conceitualizar modelos norteadores de manejo e de planejamento para cultura do milho, no intuito de obter a produtividade de grãos contemplada pelas incertezas climáticas diárias dos principais elementos do clima e suas correlações, para posteriormente se obter as correspondentes necessidades de água e de nitrogênio pela cultura. Para tanto, um experimento de campo foi conduzido, informações da literatura foram revisadas e levantadas, e modelos de previsão foram concebidos para a produtividade de grãos e para as demais variáveis de interesse. Como principais resultados, obteve-se: (i) sob condições adequadas de suprimento hídrico e de nitrogênio, o híbrido DKB-390 requer cerca de 573 litros de água para kg de grão que produz; (ii) o genótipo responde significativamente à segunda cobertura com nitrogênio, caso a cultura seja conduzida sob elevada população de plantas e adequado suprimento hídrico; (iii) a segunda cobertura com nitrogênio promoveu melhor manutenção da área foliar durante a fase de enchimento de grãos; (iv) o incremento da segunda cobertura de nitrogênio promoveu maior eficiência de uso da água pela cultura, bem como um leve aumento nos valores modais do número de grãos por fileira (da espiga) e da massa de 1000 grãos; (v) sob condições de adequado suprimento hídrico, o coeficiente de extinção médio, generalizado para todo o ciclo, é da ordem de 0,4267; valor que tende a ser maior na medida em que o suprimento de nitrogênio é menor; (vi) a eficiência de uso da radiação foi calculada em 3,52 g (fitomassa seca de parte aérea) MJ-1 (radiação solar fotossinteticamente ativa interceptada), tendo sido menor em função do emprego do regime de nitrogênio mais restritivo; (vii) os coeficientes de cultura obtidos do experimento podem ser utilizados para o manejo da irrigação do híbrido DKB-390, para os principais subperíodos, para que a produtividade não seja penalizada por déficit hídrico; (viii) o índice de colheita (expresso em relação à parte aérea) foi da ordem de 40% (variando entre 37% e 43%) sob condições de suprimento adequado de água e nitrogênio, valores que tenderam a ser maiores quando da restrição da segunda cobertura; (ix) o modelo determinístico proposto simulou adequadamente a evolução da produtividade de fitomassa de parte aérea do híbrido empregado, bem como sua produtividade de grãos sob adequadas condições de suprimento hídrico e de nitrogênio; (x) o modelo determinístico simulou adequadamente as evapotranspirações diárias o consumo hídrico através do método de Penman-Monteith; (xi) o modelo estocástico sugerido mostrou-se satisfatório, mediante o uso da distribuição normal bivariada das variáveis radiação solar e temperatura média do ar, para simular a produtividade de grãos sob condições de suprimento hídrico adequado e sob déficit moderado; e (xii) aparentemente, o modelo estocástico necessita ser melhorado quanto à capacidade de previsão das necessidades hídricas e de nitrogênio, pois tende claramente a subestimar as primeiras e superestimar as segundas. / Maize is on of the world most important crops, given that the products generated from this cereal are largely used by sectors like starch industry, animal and human nutrition, as well as biomass energy production and refineries. For these reasons, there is frequently a huge interest in knowing the potential adoption of the main available genotypes in relation to the environment in which they will be supposedly subjected. Considering the hybrid DKB-390 under full irrigated conditions, this work has as the central objective to characterize the most important ecophysiological attributes such as leaf area, radiation use efficiency, extinction coefficient, crop coefficients, water use and ear yield components. Additionaly, specif goals were to conceptualize models applicable for both management and planning of maize crops in order to predict the grain productivity contemplated by daily climate incertainties of the driven climate variables (i.e. radiation and temperature) and their correlation, then to achieve the water and nitrogen requirement corresponding to the predicted productivity. A field experiment was carried out, useful information from literature were obtained and reviewed, and models were created towards to support the prediction tools. The following outcomes might be highligthed: (i) under suitable conditions of both nitrogen and water supply, hybrid DKB-390 requires about 573 litters of water per each kilogram of produced grain; (ii) the genotype is significantly responsive to the second nitrogen covering when growing under high plant population and suitable water supply; (iii) the second nitrogen covering has enhanced better leaf area maintainance during grain filling stage; (iv) the second nitrogen covering has led to a better water use efficiency, as well as slightly increased modal values of the number of kernels per row (of ear) and the mass of a thousand kernels; (v) under suitable water supply, averaged extinction coefficient might be generalized as 0.4267 throughout the whole cycle, whereas tending to be higher as the nitrogen supply is restricted; (vi) the radiation use efficiency as calculated as 3.52 g (above-ground dry matter) MJ-1 (intercepted photossyntheticaly active radiation), being smaller as the nitrogen supply is restricted; (vii) some crop coefficients were found for the main phenological stages and may be adopted for irrigation management of hybrid DKB-390, when one aims to not deplet the productivity; (viii) the harvest index (above-ground based) was found about 40% (varying from 37% to 43%) if water and nitrogen are added sufficiently, and is likely to be higher provided that the second covering is not done; (ix) the proposed determinist model has performed well when simulating above-ground dry matter time course and its corresponding grain productivity under full and moderated water deficit conditions; (x) by using Penman-Montheit method, the deterministic model apparently simulates well both daily evapotranspiration and water uses; (xi) through bivariate normal distribution of averaged daily solar radiation and air temperature, the suggested stochastic model has simulated grain productivity in a satisfactory way; and (xii) the suggested stochastic model need to be improved in terms of its water and nitrogen requirement predictability, given that it clearly tends to underestimate the former and overestimate the latter.

Neste trabalho foi proposto um modelo de regressão para dados com censura intervalar utilizando a distribuição Weibull-exponenciada, que possui como característica principal a função de taxa de falha que assume diferentes formas (unimodal, forma de banheira, crescente e decrescente). O atrativo desse modelo de regressão é a sua utilização para discriminar modelos, uma vez que o mesmo possui como casos particulares os modelos de regressão Exponencial, Weibull, Exponencial-exponenciada, entre outros. Também foi estudado um modelo de regressão para dados de sobrevivência grupados na qual a abordagem é fundamentada em modelos de tempo discreto e em tabelas de vida. A estrutura de regressão representada por uma probabilidade é modelada adotando-se diferentes funções de ligação, tais como, logito, complemento log-log, log-log e probito. Em ambas as pesquisas, métodos de validação dos modelos estatísticos propostos são descritos e fundamentados na análise de sensibilidade. Para detectar observações influentes nos modelos propostos, foram utilizadas medidas de diagnóstico baseadas na deleção de casos, denominadas de influência global e medidas baseadas em pequenas perturbações nos dados ou no modelo proposto, denominada de influência local. Para verificar a qualidade de ajuste do modelo e detectar pontos discrepantes foi realizada uma análise de resíduos nos modelos propostos. Os resultados desenvolvidos foram aplicados a dois conjuntos de dados reais. / In this study, a regression model for interval-censored data were developed, using the Exponentiated- Weibull distribution, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease). A good feature of that regression model is their use to discriminate models, that have as particular cases, the models of regression: Exponential, Weibull, Exponential-exponentiated, amongst others. Also a regression model were studied for grouped survival data in which the approach is based in models of discrete time and in life tables, the regression structure represented by a probability is modeled through the use of different link function, logit, complementary log-log, log-log or probit. In both studies, validation methods for the statistical models studied are described and based on the sensitivity analysis. To find influential observations in the studied models, diagnostic measures were used based on case deletion, denominated as global influence and measures based on small perturbations on the data or in the studied model, denominated as local influence. To verify the goodness of fitting of the model and to detect outliers it was performed residual analysis for the proposed models. The developed results were applied to two real data sets.

This dissertation investigates the learning scenarios where a high-dimensional parameter has to be estimated from a given sample of fixed size, often smaller than the dimension of the problem. The first part answers some open questions for the binary classification problem in the framework of active learning. Given a random couple (X,Y) with unknown distribution P, the goal of binary classification is to predict a label Y based on the observation X. Prediction rule is constructed from a sequence of observations sampled from P. The concept of active learning can be informally characterized as follows: on every iteration, the algorithm is allowed to request a label Y for any instance X which it considers to be the most informative. The contribution of this work consists of two parts: first, we provide the minimax lower bounds for the performance of active learning methods. Second, we propose an active learning algorithm which attains nearly optimal rates over a broad class of underlying distributions and is adaptive with respect to the unknown parameters of the problem. The second part of this thesis is related to sparse recovery in the framework of dictionary learning. Let (X,Y) be a random couple with unknown distribution P. Given a collection of functions H, the goal of dictionary learning is to construct a prediction rule for Y given by a linear combination of the elements of H. The problem is sparse if there exists a good prediction rule that depends on a small number of functions from H. We propose an estimator of the unknown optimal prediction rule based on penalized empirical risk minimization algorithm. We show that the proposed estimator is able to take advantage of the possible sparse structure of the problem by providing probabilistic bounds for its performance.

The study of biological diversity has seen a tremendous growth over the past few decades. Among the commonly used indices capturing both the richness and evenness of a community, the Berger-Parker index, which relates to the maximum proportion of all species, is particularly effective. However, when the number of individuals and species grows without bound this index changes, and it is important to develop statistical tools to measure this change. In this thesis, we introduce two estimators for this maximum: the multinomial maximum and the length of the longest increasing subsequence. In both cases, the limiting distribution of the estimators, as the number of individuals and species simultaneously grows without bound, is obtained. Then, constructing the 95% confidence intervals for the maximum proportion helps improve the comparison of the Berger-Parker index among communities. Finally, we compare the two approaches by examining their associated bias corrected estimators and apply our results to environmental data.

El concepto de dependencia aparece por todas partes en nuestra tierra y sus habitantes de manera profunda. Son innumerables los ejemplos de fenómenos interdependientes en la naturaleza, así como en aspectos médicos, sociales, políticos, económicos, entre otros. Más aún, la dependencia es obviamente no determinística, sino de naturaleza estocástica. Es por lo anterior que resulta sorprendente que conceptos y medidas de dependencia no hayan recibido suficiente atención en la literatura estadística. Al menos hasta 1966, cuando el trabajo pionero de E.L. Lehmann probó el lema de Hoeffding. Desde entonces, se han publicado algunas generalizaciones de este. Nosotros hemos obtenido una generalización multivariante para funciones de variación acotada que agrupa a las planteadas anteriormente, al establecer la relación entre los planteamiento presentados por Quesada-Molina (1992) y Cuadras (2002b) y extendiendo este último al caso multivariante. Uno de los conceptos importante en la interpretación estadística esta relacionada con la dimensión. Es por eso que hemos definido la dimensionalidad geométrica de una distribución conjunta H en función del cardinal del conjunto de correlaciones canónicas de H, si H se puede representar mediante una expansión diagonal. La dimensionalidad geométrica ha sido obtenida para algunas de las familias de cópulas más conocidas. Para determinar la dimensionalidad de algunas de las copulas, se utilizaron métodos numéricos. De acuerdo con la dimensionalidad, hemos clasificado a las cópulas en cuatro grupos: las de dimensión cero, finita, numerable o continua. En la mayoría de las cópulas se encontro que poseen dimensión numerable. Con el uso de dos funciones que satisfacen ciertas condiciones de regularidad, se ha obtenido una extensión generalizada para la cópula Gumbel-Barnett, a la que hemos deducido sus principales propiedades y medidas de dependencia para algunas funciones en particular. La cópula FGM es una de las cópulas con más aplicabilidad en campos como el análisis financiero, y a la que se le han obtenido un gran número de generalizaciones para el caso simétrico. Nosotros hemos obtenido dos nuevas generalizaciones. La primera fue obtenida al adicionar dos distribuciones auxiliares y la segunda generalización es para el caso asimétrico. En está última caben algunas de las generalizaciones existentes. Para ambos casos se han deducido los rangos admisibles de los parámetros de asociación, las principales propiedades y las medidas de dependencia. Demostramos que si se conocen las funciones canónicas de una función de distribución, es posible aproximarla a otra función de distribución a través de combinaciones lineales de las funciones canónicas. Como ejemplo, consideramos la cópula FGM en dos dimensiones, en el sentido geométrico, debido a que se conocen sus funciones canónicas, y hemos comprobado numéricamente que su aproximación a otras cópulas con dimensión numerable es aceptablemente bueno. / Contributions to Dependence and Dimensionality in copulas The concept of dependency is everywhere in our land and its inhabitants in a profound way. There are countless examples of interdependent phenomena in nature, or related to medical, social, political and economic aspects. Moreover, dependence is obviously non deterministic, but stochastic in nature. For this reason, it is surprising that concepts and measures of dependence have not been paid enough attention in the statistical literature; at least until 1966 when the pioneering work of E.L. Lehmann proved Hoeffding’s lemma, some generalizations of this have been released since then. We have obtained a multivariate generalization for functions of bounded variation that groups the above mentioned generalizations, by ascertaining the relation between the approaches presented by Quesada-Molina (1992) and Cuadras (2002b) and extending the latter to the multivariate case. One of the important concepts in statistical interpretation deals with dimensionality, which is why we have defined the geometric dimensionality of a joint distribution H as a function of the cardinal of the set of canonical correlations of H, if H can be represented by a diagonal expansion. The geometrical dimensionality has been obtained for some of the best known families of copulas. To determine the dimensionality of some copulas, numerical methods were used. According to the dimensionality, we have classified the copulas into four groups: the zero-, finite-, countable- or continuous-dimensional. Most of the copulas were found to possess countable dimension. With the use of two functions that satisfy certain regularity conditions, we have obtained a generalized extension of the Gumbel-Barnett copula, for which we have derived its main properties and measures of dependence, particularly for some functions. The FGM copula is one of the copulas with more applicability in fields such as financial analysis, and for which a large number of generalizations for the symmetric case have been obtained. We have obtained two new generalizations: the first was obtained by adding two auxiliary distributions and the second generalization is to the asymmetric case, in the latter some existing generalizations do fit. For both cases, the allowable ranges of association parameters, as well as the main properties and dependence measures have been deducted. We show that if the canonical functions of a distribution function are known, it is possible to approximate it to another distribution function through linear combinations of canonical functions. As an example, consider the two-dimensional FGM copula, in the geometric sense, because their canonical functions are known and we have numerically found that their approximation to other copulas with countable dimension is acceptably good.

Thesis (Ph. D.)--Mississippi State University. Department of Computer Science and Engineering. / Title from title screen. Includes bibliographical references.

The heavy-tailed traffic from wireless users, caused by the emerging Internet and multimedia applications, induces extremely dynamic and variable network environment, which can fundamentally change the way in which wireless networks are conceived, designed, and operated. This thesis is concerned with modeling, analysis, and optimization of wireless networks in the presence of heavy tails. First, a novel traffic model is proposed, which captures the inherent relationship between the traffic dynamics and the joint effects of the mobility variability of network users and the spatial correlation in their observed physical phenomenon. Next, the asymptotic delay distribution of wireless users is analyzed under different traffic patterns and spectrum conditions, which reveals the critical conditions under which wireless users can experience heavy-tailed delay with significantly degraded QoS performance. Based on the delay analysis, the fundamental impact of heavy-tailed environment on network stability is studied. Specifically, a new network stability criterion, namely moment stability, is introduced to better characterize the QoS performance in the heavy-tailed environment. Accordingly, a throughput-optimal scheduling algorithm is proposed to maximize network throughput while guaranteeing moment stability. Furthermore, the impact of heavy-tailed spectrum on network connectivity is investigated. Towards this, the necessary conditions on the existence of delay-bounded connectivity are derived. To enhance network connectivity, the mobility-assisted data forwarding scheme is exploited, whose important design parameters, such as critical mobility radius, are derived. Moreover, the latency in wireless mobile networks is analyzed, which exhibits asymptotic linearity in the initial distance between mobile users.

This dissertation is concerned with the tail asymptotics of queueing networks with subexponential service time distributions. Our objective is to investigate the tail characteristics of key performance measures such as cycle times and waiting times on a variety of queueing models which may arise in many applications such as communication and manufacturing systems. First, we focus on a general class of closed feedforward fork and join queueing networks under the assumption that the service time distribution of at least one station is subexponential. Our goal is to derive the tail asymptotics of transient cycle times and waiting times. Furthermore, we argue that under certain conditions the asymptotic tail distributions remain the same for stationary cycle times and waiting times. Finally, we provide numerical experiments in order to understand how fast the convergence of tail probabilities of cycle times and waiting times is to their asymptotic counter parts. Next, we consider closed tandem queues with finite buffers between stations. We assume that at least one station has a subexponential service time distribution. We analyze this system under communication blocking and manufacturing blocking rules. We are interested in the tail asymptotics of transient cycle times and waiting times. Furthermore, we study under which conditions on system parameters a stationary regime exists and the transient results can be generalized to stationary counter parts. Finally, we provide numerical examples to understand the convergence behavior of the tail asymptotics of transient cycle times and waiting times. Finally, we study open tandem queueing networks with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. Finally, we provide numerical examples to investigate the convergence of the tail probabilities of transient response times and waiting times to their asymptotic counter parts.

Thesis (M.S.) -- Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.