The dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures. The confidence intervals are constructed by objective Bayesian methods and use the Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations and compared to the performance of nonparametric confidence intervals based on binomial proportion. In addition, techniques for change point detection are analyzed and further evaluated via Monte Carlo simulations. The effect of a change point on the interval estimators is studied both analytically and via Monte Carlo simulations.

Stein's method is a powerful technique that can be used to obtain bounds for approximation errors in a weak convergence setting. The method has been used to obtain approximation results for a number of distributions, such as the normal, Poisson and Gamma distributions. A major strength of the method is that it is often relatively straightforward to apply it to problems involving dependent random variables. In this thesis, we consider the adaptation of Stein's method to the class of Variance-Gamma distributions. We obtain a Stein equation for the Variance-Gamma distributions. Uniform bounds for the solution of the Symmetric Variance-Gamma Stein equation and its first four derivatives are given in terms of the supremum norms of derivatives of the test function. New formulas and inequalities for modified Bessel functions are obtained, which allow us to obtain these bounds. We then use local approach couplings to obtain bounds on the error in approximating two asymptotically Variance-Gamma distributed statistics by their limiting distribution. In both cases, we obtain a convergence rate of order n^-1 for suitably smooth test functions. The product of two normal random variables has a Variance-Gamma distribution and this leads us to consider the development of Stein's method to the product of r independent mean-zero normal random variables. An elegant Stein equation is obtained, which motivates a generalisation of the zero bias transformation. This new transformation has a number of interesting properties, which we exploit to prove some limit theorems for statistics that are asymptotically distributed as the product of two central normal distributions. The Variance-Gamma and Product Normal distributions arise as functions of the multivariate normal distribution. We end this thesis by demonstrating how the multivariate normal Stein equation can be used to prove limit theorems for statistics that are asymptotically distributed as a function of the multivariate normal distribution. We establish some sufficient conditions for convergence rates to be of order n^-1 for smooth test functions, and thus faster than the O(n^-1/2) rate that would arise from the Berry-Esseen Theorem. We apply the multivariate normal Stein equation approach to prove Variance-Gamma and Product Normal limit theorems, and we also consider an application to Friedman's X² statistic.

In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease) were studied. In all studies, general mathematical properties such as ordinary and incomplete moments, generating function, mean deviations, reliability, entropies, order statistics and their moments were discussed. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis and the observed information matrix is derived. It is also considered the likelihood ratio statistics and formal goodness-of-fit tests to compare all the proposed distributions with some of its sub-models and non-nested models. The developed results for all studies were applied to six real data sets. / Neste trabalho, foi proposta uma nova classe de distribuições generalizadas, baseada na distribuição Kummer beta (NG; KOTZ, 1995), que contém como casos particulares os geradores exponencializado e beta de distribuições. A principal característica da nova família de distribuições é fornecer grande flexibilidade para as extremidades da função densidade e portanto, ela torna-se adequada para a análise de conjuntos de dados com alto grau de assimetria e curtose. Também foram estudadas duas novas distribuições que pertencem à nova família de distribuições, baseadas nas distribuições Birnbaum-Saunders e gama generalizada, que possuem função de taxas de falhas que assumem diferentes formas (unimodal, forma de banheira, crescente e decrescente). Em todas as pesquisas, propriedades matemáticas gerais como momentos ordinários e incompletos, função geradora, desvios médio, confiabilidade, entropias, estatísticas de ordem e seus momentos foram discutidas. A estimação dos parâmetros é abordada pelo método da máxima verossimilhança e pela análise bayesiana e a matriz de informação observada foi derivada. Considerou-se, também, a estatística de razão de verossimilhanças e testes formais de qualidade de ajuste para comparar todas as distribuições propostas com alguns de seus submodelos e modelos não encaixados. Os resultados desenvolvidos foram aplicados a seis conjuntos de dados.

In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease) were studied. In all studies, general mathematical properties such as ordinary and incomplete moments, generating function, mean deviations, reliability, entropies, order statistics and their moments were discussed. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis and the observed information matrix is derived. It is also considered the likelihood ratio statistics and formal goodness-of-fit tests to compare all the proposed distributions with some of its sub-models and non-nested models. The developed results for all studies were applied to six real data sets. / Neste trabalho, foi proposta uma nova classe de distribuições generalizadas, baseada na distribuição Kummer beta (NG; KOTZ, 1995), que contém como casos particulares os geradores exponencializado e beta de distribuições. A principal característica da nova família de distribuições é fornecer grande flexibilidade para as extremidades da função densidade e portanto, ela torna-se adequada para a análise de conjuntos de dados com alto grau de assimetria e curtose. Também foram estudadas duas novas distribuições que pertencem à nova família de distribuições, baseadas nas distribuições Birnbaum-Saunders e gama generalizada, que possuem função de taxas de falhas que assumem diferentes formas (unimodal, forma de banheira, crescente e decrescente). Em todas as pesquisas, propriedades matemáticas gerais como momentos ordinários e incompletos, função geradora, desvios médio, confiabilidade, entropias, estatísticas de ordem e seus momentos foram discutidas. A estimação dos parâmetros é abordada pelo método da máxima verossimilhança e pela análise bayesiana e a matriz de informação observada foi derivada. Considerou-se, também, a estatística de razão de verossimilhanças e testes formais de qualidade de ajuste para comparar todas as distribuições propostas com alguns de seus submodelos e modelos não encaixados. Os resultados desenvolvidos foram aplicados a seis conjuntos de dados.

Muitos equipamentos utilizados para quantificar substâncias, como toxinas em alimentos, freqüentemente apresentam deficiências para quantificar quantidades baixas. Em tais casos, geralmente indicam a ausência da substância quando esta existe, mas está abaixo de um valor pequeno \'ksi\' predeterminado, produzindo valores iguais a zero não necessariamente verdadeiros. Em outros casos, detectam a presença da substância, mas são incapazes de quantificá-la quando a quantidade da substância está entre \'ksai\' e um valor limiar \'tau\', conhecidos. Por outro lado, quantidades acima desse valor limiar são quantificadas de forma contínua, dando origem a uma variável aleatória contínua X cujo domínio pode ser escrito como a união dos intervalos, [ómicron, \"ksai\'), [\"ksai\', \'tau\' ] e (\'tau\', ?), sendo comum o excesso de valores iguais a zero. Neste trabalho, são propostos modelos que possibilitam discriminar a probabilidade de zeros verdadeiros, como o modelo de mistura com dois componentes, sendo um degenerado em zero e outro com distribuição contínua, sendo aqui consideradas as distribuições: exponencial, de Weibull e gama. Em seguida, para cada modelo, foram observadas suas características, propostos procedimentos para estimação de seus parâmetros e avaliados seus potenciais de ajuste por meio de métodos de simulação. Finalmente, a metodologia desenvolvida foi ilustrada por meio da modelagem de medidas de contaminação com aflatoxina B1, observadas em grãos de milho, de três subamostras de um lote de milho, analisados no Laboratório de Micotoxinas do Departamento de Agroindústria, Alimentos e Nutrição da ESALQ/USP. Como conclusões, na maioria dos casos, as simulações indicaram eficiência dos métodos propostos para as estimações dos parâmetros dos modelos, principalmente para a estimativa do parâmetro \'delta\' e do valor esperado, \'Epsilon\' (Y). A modelagem das medidas de aflatoxina, por sua vez, mostrou que os modelos propostos são adequados aos dados reais, sendo que o modelo de mistura com distribuição de Weibull, entretanto, ajustou-se melhor aos dados. / Much equipment used to quantify substances, such as toxins in foods, is unable to measure low amounts. In cases where the substance exists, but in an amount below a small fixed value \'ksi\' , the equipment usually indicates that the substance is not present, producing values equal to zero. In cases where the quantity is between \'\'ksi\' and a known threshold value \'tau\', it detects the presence of the substance but is unable to measure the amount. When the substance exists in amounts above the threshold value ?, it is measure continuously, giving rise to a continuous random variable X whose domain can be written as the union of intervals, [ómicron, \"ksai\'), [\"ksai\', \'tau\' ] and (\'tau\', ?), This random variable commonly has an excess of zero values. In this work we propose models that can detect the probability of true zero, such as the mixture model with two components, one being degenerate at zero and the other with continuous distribution, where we considered the distributions: exponential, Weibull and gamma. Then, for each model, its characteristics were observed, procedures for estimating its parameters were proposed and its potential for adjustment by simulation methods was evaluated. Finally, the methodology was illustrated by modeling measures of contamination with aflatoxin B1, detected in grains of corn from three sub-samples of a batch of corn analyzed at the laboratory of of Mycotoxins, Department of Agribusiness, Food and Nutrition ESALQ/USP. In conclusion, in the majority of cases the simulations indicated that the proposed methods are efficient in estimating the parameters of the models, in particular for estimating the parameter ? and the expected value, E(Y). The modeling of measures of aflatoxin, in turn, showed that the proposed models are appropriate for the actual data, however the mixture model with a Weibull distribution fits the data best.

本論文在Li(2000)的Gaussian Copula的背景之下，將資產價值服從常態分配的假設改為服從Variance Gamma分配，利用Copula模型模擬債權群組內各個標的資產的違約時點，並利用蒙地卡羅抽取亂數的方法，取平均之後求得信用連結債券所連結的資產債權組合價值。除此之外，本論文比較假設資產價值服從常態分配、Student t分配和Variance Gamma分配下，計算求得的資產池價值。實證結果顯示，假設服從Variance Gamma分配最接近市場的真實違約資料。這是由於Variance Gamma分配具備Student t分配的厚尾性質，能有效捕捉常態分配缺少的尾端損失機率，並可調整偏態係數和峰態係數，可以求出更接近市場價值的評價結果。最後，在敏感度分析方面，改變影響資產池價值的兩大因子：平均違約回收率和資產間相關係數。結果顯示，當平均違約回收率高於0.7時，相關係數越高的債權群組，其資產池價值亦越高。若平均違約回收率越低且資產間相關係數越高的話，越容易出現一起違約的現象，因此資產池價值會下降。因此投資人在挑選信用連結債券時，應注意所連結的標的資產群組內資產報酬的相關性，最好避免相關性高的資產群組，以免金融海嘯來臨的時候，多個資產同時違約的情形發生。

在探討願付價格的條件評估法中一種常被使用的方法為“雙界二分選擇法”，並且一個隱含的假設是，所有研究對象皆願意支付一個合理的金額。然而對於某些商品，有些人也許願意支付任何金額；相對的，有些人可能不願意支付任何金額。分析願付價格時若不考慮這兩類極端反應者，則可能會得到一個偏誤的願付價格。本篇研究中，我們提出一個“混合模型”來處理此議題，其中以多元邏輯斯迴歸模型來描述不同反應者的比例，並以加速失敗時間模型來估計願意支付合理金額者其願付價格的分布。此外，我們以關於治療高血壓新藥之願付價格實例，作為實證分析。 / One commonly used method in contingent valuation (CV) survey for WTP (willingness-to-pay) is the “double-bound dichotomous choice approach” and an implicit assumption is that all study subjects are willing to pay a reasonable price. However, for certain goods, some subjects may be willing to pay any price for them, while some others may be unwilling to pay any price. Without considering these two types of the extreme respondents, a wrongly estimated WTP value will be obtained. We propose a “mixture model” to handle the issues in this study, in which a multinomial logistic model is taken to specify the proportions of different respondents and an accelerated failure time model is utilized to describe the distribution of WTP price for subjects who are willing to pay a reasonable price. In addition, an empirical example on WTP prices for a new hypertension treatment is provided to illustrate the proposed methods.

Made available in DSpace on 2014-06-11T19:31:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-05-05Bitstream added on 2014-06-13T20:02:21Z : No. of bitstreams: 1 rickli_li_dr_botfca.pdf: 601367 bytes, checksum: abdaa96dc222f7b27de2cdeb6898ad34 (MD5) / Universidade Estadual Paulista (UNESP) / O aumento populacional do planeta tem exigido cada vez mais produtividade na agricultura objetivando suprir suas necessidades alimenticias. Um dos mais importantes fatores que determinam o sucesso ou o fracasso desta producao sao as variaveis climaticas, dentre elas, pode-se citar a precipitacao pluviometrica. A presente pesquisa analisou a eficiencia dos fatores funcionais no processo de simulacao de dados diarios de precipitacao utilizando a distribuicao Gama. Foram utilizadas series climatologicas diarias para as localidades de Piracicaba . SP e Ponta Grossa . PR. Para determinacao dos estimadores dos parametros da distribuicao Gama (ãá e ãâ), foram avaliados os procedimentos baseados no metodo dos momentos, da verossimilhanca e o metodo numerico de Greenwood & Durand. Avaliou-se tres geradores de numeros pseudo-aleatorios congruencias e dois algoritmos computacionais para geracao da variavel aleatorias Gama que foram implementados no simulador Sedac_R. Por meio de procedimentos estatisticos a validacao apontou que a escolha adequada do metodo para estimativa dos parametros da distribuicao Gama e o algoritmo computacional para geracao da variavel aleatoria Gama devem ser levados em consideracao na simulacao de series climaticas de precipitacao. Em relacao ao gerador de numeros pseudo-aleatorios os resultados indicaram... / The increase of people in the planet has required more productivity in the agriculture field in order to supply the food need. One of the most important factors that determine the success or the failures of that productivity are the climatic variables, such as the rain precipitation. This research analyzed the efficiency of the functional factors in the precipitation daily data simulation process, using the Gamma distribution. Daily climatic series related to the Piracicaba - SP and Ponta Grossa - PR cities were used. The procedures based on the Greenwood & Durand numerical, Likelihood and Moment methods were evaluated aiming to determine the approximation of the parameters of the Gamma distribution (á and â). Three congruent pseudorandom generators and two computational algorithms to generate the Gamma random variable implemented in the Sedac_R simulator were evaluated. By way of statistics procedures, the validation indicated that the suitable choose to both the approximation method of the parameters of the Gamma distribution (á and â) and the computational algorithm to generate the Gamma random variable must be taken into consideration in the precipitation climatic series simulation. Related to the numerical pseudo-random generator the results showed that it doesn t interferes in the accuracy of the generated data.

Submitted by Karlla Delalibera Chagas null (karlladelalibera@gmail.com) on 2018-05-14T12:25:13Z No. of bitstreams: 1 dissertação - Karlla Delalibera.pdf: 2936984 bytes, checksum: 3d99ddd54b4c7d3230e5de9070915594 (MD5) / Approved for entry into archive by Claudia Adriana Spindola null (claudia@fct.unesp.br) on 2018-05-14T12:53:09Z (GMT) No. of bitstreams: 1 chagas_kd_me_prud.pdf: 2936984 bytes, checksum: 3d99ddd54b4c7d3230e5de9070915594 (MD5) / Made available in DSpace on 2018-05-14T12:53:09Z (GMT). No. of bitstreams: 1 chagas_kd_me_prud.pdf: 2936984 bytes, checksum: 3d99ddd54b4c7d3230e5de9070915594 (MD5) Previous issue date: 2018-04-16 / Pró-Reitoria de Pós-Graduação (PROPG UNESP) / Neste trabalho iremos realizar uma abordagem sobre a modelagem de dados que advém de um teste acelerado. Consideraremos o caso em que a carga de estresse aplicada foi do tipo "step-stress". Para a modelagem, utilizaremos os modelos step-stress simples e múltiplo sob censura tipo II e censura progressiva tipo II, e iremos supor que os tempos de vida dos itens em teste seguem uma distribuição Gama. Além disso, também será utilizado o modelo step-stress simples sob censura tipo II considerando a presença de riscos competitivos. Será realizada uma abordagem clássica, por meio do método de máxima verossimilhança e uma abordagem Bayesiana usando prioris não-informativas, para estimar os parâmetros dos modelos. Temos como objetivo realizar a comparação dessas duas abordagens por meio de simulações para diferentes tamanhos amostrais e utilizando diferentes funções de perda (Erro Quadrático, Linex, Entropia), e através de estatísticas verificaremos qual desses métodos se aproxima mais dos verdadeiros valores dos parâmetros. / In this work, we will perform an approach to data modeling that comes from an accelerated test. We will consider the case where the stress load applied was of the step-stress type. For the modeling, we will use the simple and multiple step-stress models under censorship type II and progressive censorship type II, and we will assume that the lifetimes of the items under test follow a Gamma distribution. In addition, the simple step-stress model under censorship type II will also be used considering the presence of competitive risks. A classical approach will be performed, using the maximum likelihood method and a Bayesian approach using non-informative prioris, to estimate the parameters of the models. We aim to compare these two approaches by simulations for different sample sizes and using different loss functions (Quadratic Error, Linex, Entropy), and through statistics, we will check which of these approaches is closer to the true values of the parameters.

Resumo: O aumento populacional do planeta tem exigido cada vez mais produtividade na agricultura objetivando suprir suas necessidades alimenticias. Um dos mais importantes fatores que determinam o sucesso ou o fracasso desta producao sao as variaveis climaticas, dentre elas, pode-se citar a precipitacao pluviometrica. A presente pesquisa analisou a eficiencia dos fatores funcionais no processo de simulacao de dados diarios de precipitacao utilizando a distribuicao Gama. Foram utilizadas series climatologicas diarias para as localidades de Piracicaba . SP e Ponta Grossa . PR. Para determinacao dos estimadores dos parametros da distribuicao Gama (ãá e ãâ), foram avaliados os procedimentos baseados no metodo dos momentos, da verossimilhanca e o metodo numerico de Greenwood & Durand. Avaliou-se tres geradores de numeros pseudo-aleatorios congruencias e dois algoritmos computacionais para geracao da variavel aleatorias Gama que foram implementados no simulador Sedac_R. Por meio de procedimentos estatisticos a validacao apontou que a escolha adequada do metodo para estimativa dos parametros da distribuicao Gama e o algoritmo computacional para geracao da variavel aleatoria Gama devem ser levados em consideracao na simulacao de series climaticas de precipitacao. Em relacao ao gerador de numeros pseudo-aleatorios os resultados indicaram... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The increase of people in the planet has required more productivity in the agriculture field in order to supply the food need. One of the most important factors that determine the success or the failures of that productivity are the climatic variables, such as the rain precipitation. This research analyzed the efficiency of the functional factors in the precipitation daily data simulation process, using the Gamma distribution. Daily climatic series related to the Piracicaba - SP and Ponta Grossa - PR cities were used. The procedures based on the Greenwood & Durand numerical, Likelihood and Moment methods were evaluated aiming to determine the approximation of the parameters of the Gamma distribution (á and â). Three congruent pseudorandom generators and two computational algorithms to generate the Gamma random variable implemented in the Sedac_R simulator were evaluated. By way of statistics procedures, the validation indicated that the suitable choose to both the approximation method of the parameters of the Gamma distribution (á and â) and the computational algorithm to generate the Gamma random variable must be taken into consideration in the precipitation climatic series simulation. Related to the numerical pseudo-random generator the results showed that it doesn’t interferes in the accuracy of the generated data. / Orientador: Ângelo Catâneo / Coorientador: Jorim Souza Virgens Filho / Banca: Célia Regina Lopes Zimback / Banca: Manoel Henrique Salgado / Banca: Marcelo Giovaneti Canteri / Banca: José Fernando Mantovani Micali / Doutor