Global ETD Search

51	Conditions d'existence des processus déterminantaux et permanentaux / Existence conditions for determinantal and permanental processes Maunoury, Franck 27 March 2018 (has links) Nous établissons des conditions nécessaires et suffisantes d’existence et d’infinie divisibilité pour des processus ponctuels alpha-déterminantaux et, lorsque alpha est positif, pour leur intensité sous-jacente (en tant que processus de Cox). Dans le cas où l’espace est fini, ces distributions correspondent à des lois binomiales, négatives binomiales et gamma multidimensionnelles. Nous étudions de façon approfondie ces deux derniers cas avec un noyau non nécessairement symétrique. / We establish necessary and sufficient conditions for the existence and infinite divisibility of alpha-determinantal processes and, when alpha is positive, of their underlying intensity (as Cox process). When the space is finite, these distributions correspond to multidimensional binomial, negative binomial and gamma distributions. We make an in-depth study of these last two cases with a non necessarily symmetric kernel. Processus alpha-déterminantaux Infinie divisibilité Vecteur permanental Loi gamma multidimensionnelle M-matrice Vecteur gaussien Cycles de matrice Permanental processes (or Boson process) Alpha-determinantal Complete monotonicity Permanental vector Multivariate gamma distribution M-matrix Gaussian vector Matrix cycles Infinite divisibility
52	CURE RATE AND DESTRUCTIVE CURE RATE MODELS UNDER PROPORTIONAL ODDS LIFETIME DISTRIBUTIONS FENG, TIAN January 2019 (has links) Cure rate models, introduced by Boag (1949), are very commonly used while modelling lifetime data involving long time survivors. Applications of cure rate models can be seen in biomedical science, industrial reliability, finance, manufacturing, demography and criminology. In this thesis, cure rate models are discussed under a competing cause scenario, with the assumption of proportional odds (PO) lifetime distributions for the susceptibles, and statistical inferential methods are then developed based on right-censored data. In Chapter 2, a flexible cure rate model is discussed by assuming the number of competing causes for the event of interest following the Conway-Maxwell (COM) Poisson distribution, and their corresponding lifetimes of non-cured or susceptible individuals can be described by PO model. This provides a natural extension of the work of Gu et al. (2011) who had considered a geometric number of competing causes. Under right censoring, maximum likelihood estimators (MLEs) are obtained by the use of expectation-maximization (EM) algorithm. An extensive Monte Carlo simulation study is carried out for various scenarios, and model discrimination between some well-known cure models like geometric, Poisson and Bernoulli is also examined. The goodness-of-fit and model diagnostics of the model are also discussed. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. Next, in Chapter 3, the destructive cure rate models, introduced by Rodrigues et al. (2011), are discussed under the PO assumption. Here, the initial number of competing causes is modelled by a weighted Poisson distribution with special focus on exponentially weighted Poisson, length-biased Poisson and negative binomial distributions. Then, a damage distribution is introduced for the number of initial causes which do not get destroyed. An EM-type algorithm for computing the MLEs is developed. An extensive simulation study is carried out for various scenarios, and model discrimination between the three weighted Poisson distributions is also examined. All the models and methods of estimation are evaluated through a simulation study. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. In Chapter 4, frailty cure rate models are discussed under a gamma frailty wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution in which the lifetimes of non-cured individuals can be described by PO model. The detailed steps of the EM algorithm are then developed for this model and an extensive simulation study is carried out to evaluate the performance of the proposed model and the estimation method. A cutaneous melanoma dataset as well as a simulated data are used for illustrative purposes. Finally, Chapter 5 outlines the work carried out in the thesis and also suggests some problems of further research interest. / Thesis / Doctor of Philosophy (PhD) Cure rate models Mixture model Long-term survivors COM-Poisson distribution Weighted Poisson distribution EM algorithm Right censoring Non-informative censoring Profile likelihood Asymptotic variances and covariances Maximum likelihood estimation Likelihood-ratio test Exponential distribution Proportional odds model Weibull distribution Log-logistic distribution Gamma distribution Mixture of chi-square Akaike Information Criterion (AIC) Bayesian Information Criterion (BIC) Model discrimination Monte Carlo simulations Goodness-of-fit test Cutaneous melanoma
53	Introduction to Probability Theory Chen, Yong-Yuan 25 May 2010 (has links) In this paper, we first present the basic principles of set theory and combinatorial analysis which are the most useful tools in computing probabilities. Then, we show some important properties derived from axioms of probability. Conditional probabilities come into play not only when some partial information is available, but also as a tool to compute probabilities more easily, even when partial information is unavailable. Then, the concept of random variable and its some related properties are introduced. For univariate random variables, we introduce the basic properties of some common discrete and continuous distributions. The important properties of jointly distributed random variables are also considered. Some inequalities, the law of large numbers and the central limit theorem are discussed. Finally, we introduce additional topics the Poisson process. Chebyshev¡¦s inequality central limit theorem Poisson process Markov¡¦s inequality multivariate normal distribution multinomial distribution F distribution t distribution chi-square distribution lognormal distribution Beta distribution Cauchy distribution Weibull distribution gamma distribution exponential distribution normal distribution discrete uniform distribution uniform distribution hypergeometric distribution geometric distribution negative binomial distribution Poisson distribution binomial distribution Bernoulli distribution Bayes theorem theorem of total probability axioms of probability multinomial theorem inclusion-exclusion principle set
54	Análise de carteiras em tempo discreto / Discrete time portfolio analysis Kato, Fernando Hideki 14 April 2004 (has links) Nesta dissertação, o modelo de seleção de carteiras de Markowitz será estendido com uma análise em tempo discreto e hipóteses mais realísticas. Um produto tensorial finito de densidades Erlang será usado para aproximar a densidade de probabilidade multivariada dos retornos discretos uniperiódicos de ativos dependentes. A Erlang é um caso particular da distribuição Gama. Uma mistura finita pode gerar densidades multimodais não-simétricas e o produto tensorial generaliza este conceito para dimensões maiores. Assumindo que a densidade multivariada foi independente e identicamente distribuída (i.i.d.) no passado, a aproximação pode ser calibrada com dados históricos usando o critério da máxima verossimilhança. Este é um problema de otimização em larga escala, mas com uma estrutura especial. Assumindo que esta densidade multivariada será i.i.d. no futuro, então a densidade dos retornos discretos de uma carteira de ativos com pesos não-negativos será uma mistura finita de densidades Erlang. O risco será calculado com a medida Downside Risk, que é convexa para determinados parâmetros, não é baseada em quantis, não causa a subestimação do risco e torna os problemas de otimização uni e multiperiódico convexos. O retorno discreto é uma variável aleatória multiplicativa ao longo do tempo. A distribuição multiperiódica dos retornos discretos de uma seqüência de T carteiras será uma mistura finita de distribuições Meijer G. Após uma mudança na medida de probabilidade para a composta média, é possível calcular o risco e o retorno, que levará à fronteira eficiente multiperiódica, na qual cada ponto representa uma ou mais seqüências ordenadas de T carteiras. As carteiras de cada seqüência devem ser calculadas do futuro para o presente, mantendo o retorno esperado no nível desejado, o qual pode ser função do tempo. Uma estratégia de alocação dinâmica de ativos é refazer os cálculos a cada período, usando as novas informações disponíveis. Se o horizonte de tempo tender a infinito, então a fronteira eficiente, na medida de probabilidade composta média, tenderá a um único ponto, dado pela carteira de Kelly, qualquer que seja a medida de risco. Para selecionar um dentre vários modelos de otimização de carteira, é necessário comparar seus desempenhos relativos. A fronteira eficiente de cada modelo deve ser traçada em seu respectivo gráfico. Como os pesos dos ativos das carteiras sobre estas curvas são conhecidos, é possível traçar todas as curvas em um mesmo gráfico. Para um dado retorno esperado, as carteiras eficientes dos modelos podem ser calculadas, e os retornos realizados e suas diferenças ao longo de um backtest podem ser comparados. / In this thesis, Markowitzs portfolio selection model will be extended by means of a discrete time analysis and more realistic hypotheses. A finite tensor product of Erlang densities will be used to approximate the multivariate probability density function of the single-period discrete returns of dependent assets. The Erlang is a particular case of the Gamma distribution. A finite mixture can generate multimodal asymmetric densities and the tensor product generalizes this concept to higher dimensions. Assuming that the multivariate density was independent and identically distributed (i.i.d.) in the past, the approximation can be calibrated with historical data using the maximum likelihood criterion. This is a large-scale optimization problem, but with a special structure. Assuming that this multivariate density will be i.i.d. in the future, then the density of the discrete returns of a portfolio of assets with nonnegative weights will be a finite mixture of Erlang densities. The risk will be calculated with the Downside Risk measure, which is convex for certain parameters, is not based on quantiles, does not cause risk underestimation and makes the single and multiperiod optimization problems convex. The discrete return is a multiplicative random variable along the time. The multiperiod distribution of the discrete returns of a sequence of T portfolios will be a finite mixture of Meijer G distributions. After a change of the distribution to the average compound, it is possible to calculate the risk and the return, which will lead to the multiperiod efficient frontier, where each point represents one or more ordered sequences of T portfolios. The portfolios of each sequence must be calculated from the future to the present, keeping the expected return at the desired level, which can be a function of time. A dynamic asset allocation strategy is to redo the calculations at each period, using new available information. If the time horizon tends to infinite, then the efficient frontier, in the average compound probability measure, will tend to only one point, given by the Kellys portfolio, whatever the risk measure is. To select one among several portfolio optimization models, it is necessary to compare their relative performances. The efficient frontier of each model must be plotted in its respective graph. As the weights of the assets of the portfolios on these curves are known, it is possible to plot all curves in the same graph. For a given expected return, the efficient portfolios of the models can be calculated, and the realized returns and their differences along a backtest can be compared. additive and multiplicative returns additive convolution coherent risk measures convexidade convexity convolução aditiva convolução multiplicativa critério de Kelly default risk distribuição Gama Generalizada Downside Risk Downside Risk estratégia multiperiódica finite mixture of Erlang distributions Fox H function função Fox H função Meijer G Generalized Gamma distribution Kellys criterion Laplace transform large-scale optimization Lower Partial Moment Lower Partial Moment medidas coerentes de risco Meijer G function Mellin transform mistura finita de distribuições Erlang model selection multiperiod multiperiodic strategy multiperíodo multiplicative convolution otimização de carteiras otimização em larga escala portfolio optimization portfolio selection produto tensorial retornos aditivos e multiplicativos risco de falência seleção de carteiras seleção de modelo tensor product transformada de Laplace transformada de Mellin
55	Análise de carteiras em tempo discreto / Discrete time portfolio analysis Fernando Hideki Kato 14 April 2004 (has links) Nesta dissertação, o modelo de seleção de carteiras de Markowitz será estendido com uma análise em tempo discreto e hipóteses mais realísticas. Um produto tensorial finito de densidades Erlang será usado para aproximar a densidade de probabilidade multivariada dos retornos discretos uniperiódicos de ativos dependentes. A Erlang é um caso particular da distribuição Gama. Uma mistura finita pode gerar densidades multimodais não-simétricas e o produto tensorial generaliza este conceito para dimensões maiores. Assumindo que a densidade multivariada foi independente e identicamente distribuída (i.i.d.) no passado, a aproximação pode ser calibrada com dados históricos usando o critério da máxima verossimilhança. Este é um problema de otimização em larga escala, mas com uma estrutura especial. Assumindo que esta densidade multivariada será i.i.d. no futuro, então a densidade dos retornos discretos de uma carteira de ativos com pesos não-negativos será uma mistura finita de densidades Erlang. O risco será calculado com a medida Downside Risk, que é convexa para determinados parâmetros, não é baseada em quantis, não causa a subestimação do risco e torna os problemas de otimização uni e multiperiódico convexos. O retorno discreto é uma variável aleatória multiplicativa ao longo do tempo. A distribuição multiperiódica dos retornos discretos de uma seqüência de T carteiras será uma mistura finita de distribuições Meijer G. Após uma mudança na medida de probabilidade para a composta média, é possível calcular o risco e o retorno, que levará à fronteira eficiente multiperiódica, na qual cada ponto representa uma ou mais seqüências ordenadas de T carteiras. As carteiras de cada seqüência devem ser calculadas do futuro para o presente, mantendo o retorno esperado no nível desejado, o qual pode ser função do tempo. Uma estratégia de alocação dinâmica de ativos é refazer os cálculos a cada período, usando as novas informações disponíveis. Se o horizonte de tempo tender a infinito, então a fronteira eficiente, na medida de probabilidade composta média, tenderá a um único ponto, dado pela carteira de Kelly, qualquer que seja a medida de risco. Para selecionar um dentre vários modelos de otimização de carteira, é necessário comparar seus desempenhos relativos. A fronteira eficiente de cada modelo deve ser traçada em seu respectivo gráfico. Como os pesos dos ativos das carteiras sobre estas curvas são conhecidos, é possível traçar todas as curvas em um mesmo gráfico. Para um dado retorno esperado, as carteiras eficientes dos modelos podem ser calculadas, e os retornos realizados e suas diferenças ao longo de um backtest podem ser comparados. / In this thesis, Markowitzs portfolio selection model will be extended by means of a discrete time analysis and more realistic hypotheses. A finite tensor product of Erlang densities will be used to approximate the multivariate probability density function of the single-period discrete returns of dependent assets. The Erlang is a particular case of the Gamma distribution. A finite mixture can generate multimodal asymmetric densities and the tensor product generalizes this concept to higher dimensions. Assuming that the multivariate density was independent and identically distributed (i.i.d.) in the past, the approximation can be calibrated with historical data using the maximum likelihood criterion. This is a large-scale optimization problem, but with a special structure. Assuming that this multivariate density will be i.i.d. in the future, then the density of the discrete returns of a portfolio of assets with nonnegative weights will be a finite mixture of Erlang densities. The risk will be calculated with the Downside Risk measure, which is convex for certain parameters, is not based on quantiles, does not cause risk underestimation and makes the single and multiperiod optimization problems convex. The discrete return is a multiplicative random variable along the time. The multiperiod distribution of the discrete returns of a sequence of T portfolios will be a finite mixture of Meijer G distributions. After a change of the distribution to the average compound, it is possible to calculate the risk and the return, which will lead to the multiperiod efficient frontier, where each point represents one or more ordered sequences of T portfolios. The portfolios of each sequence must be calculated from the future to the present, keeping the expected return at the desired level, which can be a function of time. A dynamic asset allocation strategy is to redo the calculations at each period, using new available information. If the time horizon tends to infinite, then the efficient frontier, in the average compound probability measure, will tend to only one point, given by the Kellys portfolio, whatever the risk measure is. To select one among several portfolio optimization models, it is necessary to compare their relative performances. The efficient frontier of each model must be plotted in its respective graph. As the weights of the assets of the portfolios on these curves are known, it is possible to plot all curves in the same graph. For a given expected return, the efficient portfolios of the models can be calculated, and the realized returns and their differences along a backtest can be compared. convexidade convolução aditiva convolução multiplicativa critério de Kelly distribuição Gama Generalizada Downside Risk estratégia multiperiódica função Fox H função Meijer G Lower Partial Moment medidas coerentes de risco mistura finita de distribuições Erlang multiperíodo otimização de carteiras otimização em larga escala produto tensorial retornos aditivos e multiplicativos risco de falência seleção de carteiras seleção de modelo transformada de Laplace transformada de Mellin additive and multiplicative returns additive convolution coherent risk measures convexity default risk Downside Risk finite mixture of Erlang distributions Fox H function Generalized Gamma distribution Kellys criterion Laplace transform large-scale optimization Lower Partial Moment Meijer G function Mellin transform model selection multiperiod multiperiodic strategy multiplicative convolution portfolio optimization portfolio selection tensor product
56	Minimization of Noise and Vibration Related to Driveline Imbalance using Robust Design Processes Al-Shubailat, Omar 17 August 2013 (has links) Variation in vehicle noise, vibration and harshness (NVH) response can be caused by variability in design (e.g. tolerance), material, manufacturing, or other sources of variation. Such variation in the vehicle response causes a higher percentage of produced vehicles to have higher levels (out of specifications) of NVH leading to higher number of warranty claims and loss of customer satisfaction, which are proven costly. Measures must be taken to ensure less warranty claims and higher levels of customer satisfactions. As a result, original equipment manufacturers (OEMs) have implemented design for variation in the design process to secure an acceptable (or within specification) response. The focus here will be on aspects of design variations that should be considered in the design process of drivelines. Variations due to imbalance in rotating components can be unavoidable or costly to control. Some of the major components in the vehicle that are known to have imbalance and traditionally cause NVH issues and concerns include the crankshaft, the drivetrain components (transmission, driveline, half shafts, etc.), and wheels. The purpose is to assess NVH as a result of driveline imbalance variations and develop a tool to help design a more robust system to such variations. program. Java quality engineering quality capability studies manufacturing processes manufacturing engineer design engineer sales profit customer concern warranty objectionable Eigen functions vectors Eigen Eigen values identity Euler differential equations differential transfer case shaft driveline static imbalance dynamic imbalance passenger customer driver inboard ear driver outboard ear steering wheel seat track variation Gamma distribution normal distribution standard deviation average variance mean phasor victor scalar linear system LTI linear time invariant transfer function output input microphone accelerometers tachometer channels order frequency frequency domain time domain convolution Transformation Fourier Transformer Fourier imaginary and real logarithmic decibel sensitivity curves run down run up two wheel drive Four Wheel Drive Nissan Truck OEM Original Equipment Manufacturers Data Acquisitions Channels Simulation Six Sigma variability Design Robust sensitivity Vibration Imbalance Noise Harshness NVH Driveline

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