Biblioteca Digital

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.; CAPES; CNPq

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP, Brazil

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.; FAPESP; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); CNPq (Brazil); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In this paper we propose a hybrid hazard regression model with threshold stress which includes the proportional hazards and the accelerated failure time models as particular cases. To express the behavior of lifetimes the generalized-gamma distribution is assumed and an inverse power law model with a threshold stress is considered. For parameter estimation we develop a sampling-based posterior inference procedure based on Markov Chain Monte Carlo techniques. We assume proper but vague priors for the parameters of interest. A simulation study investigates the frequentist properties of the proposed estimators obtained under the assumption of vague priors. Further, some discussions on model selection criteria are given. The methodology is illustrated on simulated and real lifetime data set.; CAPES; CAPES; CNPq; CNPQ

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.; DGIP (Chile); DGIP (Chile) [200921]; UBB (Chile) [0905232I]; UBB (Chile); CNPq (Brasil); CNPq (Brasil); FONDECYT (Chile) [1090411]; FONDECYT (Chile)

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.; CNPq; CNPq; CAPES; CAPES

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.; CNPq; FAPESP (Brazil)

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...

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

Pós-graduação em Agronomia (Energia na Agricultura) - FCA; 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...

In this paper distinct prior distributions are derived in a Bayesian inference of the two-parameters Gamma distribution. Noniformative priors, such as Jeffreys, reference, MDIP, Tibshirani and an innovative prior based on the copula approach are investigated. We show that the maximal data information prior provides in an improper posterior density and that the different choices of the parameter of interest lead to different reference priors in this case. Based on the simulated data sets, the Bayesian estimates and credible intervals for the unknown parameters are computed and the performance of the prior distributions are evaluated. The Bayesian analysis is conducted using the Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions under the above priors.

The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma-Weibull distribution of a random variable can be explicitely expressed in terms of the incomplete confluent Fox-Wright Psi-function, which is recently introduced by Srivastava and Pogány (2007). In the same time, we generalize certain results by Nadarajah and Kotz that follow as special cases of our findings.

The initial step in calculating the Standardized Precipitation Index (SPI) is to determine a probability density function (pdf) that describes the precipitation series under analysis. Once this pdf is determined, the cumulative probability of an observed precipitation amount is computed. The inverse normal function is then applied to the cumulative probability. The result is the SPI. This article assessed the changes in SPI final values, when computed based on Gamma 2-parameters (Gam) and Pearson Type III (PE3) distributions (SPIGam and SPIPE3, respectively). Monthly rainfall series, available from five weather stations of the State of São Paulo, were chosen for this study. Considering quantitative and qualitative assessments of goodness-of-fit (evaluated at 1-, 3-, and 6-months precipitation totals), the PE3 distribution seems to be a better choice than the Gam distribution, in describing the long-term rainfall series of the State of São Paulo. In addition, it was observed that the number of SPI time series that could be seen as normally distributed was higher when this drought index was computed from the PE3 distribution. Thus, the use of the Pearson type III distribution within the calculation algorithm of the SPI is recommended in the State of São Paulo.

The statistical inference about the reliability parameter R involving independent gamma stress and exponential strength is considered. Assuming the shape parameter of gamma is a known arbitrary real number and the scale parameters of gamma and exponential are unknown, the UMVUE and MLE of R are obtained. A pivot is proposed. Some inference about R derived from this pivot is presented. It will be shown that the pivot can be used for testing hypothesis and constructing condence interval. A procedure of constructing the condence interval for R is derived. The performances of the UMVUE and MLE are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the two estimators is about the same. The MLE is preferred because of the simplicity of its computation.

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion...

The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate $\Gamma \Gamma$ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.; Comment: 7 pages, 6 figures, accepted by IEEE Transactions on Vehicular Technology

Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we obtain a limiting distribution for a suitably normalized gamma distribution when the shape parameter tends to zero. Then this limiting distribution provides insight to the construction of a new, simple, and highly efficient acceptance--rejection algorithm. Comparisons based on acceptance rates show that the proposed procedure is more efficient than existing acceptance--rejection methods.; Comment: 7 pages, 2 figures

In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome this problem by proposing a modification in a reference priori distribution, allowing for a proper posterior distribution for the parameters of the generalized gamma distribution. We perform a simulation study in order to study the efficiency of the proposed methodology, which is also fully illustrated on a real data set.; Comment: 22 pages

The gamma density function is usually defined in interval between zero and infinity. This paper introduces an upper and a lower boundary to this distribution. The parameters which characterize the truncated gamma distribution are evaluated. A statistical test is performed on two samples of stars. A comparison with the lognormal and the four power law distribution is made.; Comment: 9 pages 4 figures

É proposto um modelo para descrever chuva diária de Piracicaba-SP em termos da sua ocorrência e da quantidade. Ambos, a ocorrência de dias com e sem chuva, quando considerados como seqüências de 31 dias a partir de determinada data, puderam ser bem representadas pela distribuição binomial negativa truncada, com parâmetros ajustados a uma função periódica com dois harmônicos. A quantidade de chuva nos dias com chuva, foi adequadamente ajustada à distribuição gama com o seu parâmetro de forma (gama) permanecendo constante mas o parâmetro de escala (beta) apresentando variação periódica que pode ser descrita por uma função com dois harmônicos. A análise dos dados mostrou que as séries de chuva de 1917 a 1944 e de 1945 a 1989, resultantes da mudança dos postos de observação, são homogêneas.; A model to describe the daily rainfall in Piracicaba, SP, Brazil, is proposed to relate the ocurrence of rainy and rainless days, and in terms of their amount. Both, the occurrence of days without and with rain, in tems of their sequences of 31 days following a given date, can well be represented by the truncated negative binomial distribution function with its parameters adjusted to a periodic funtion with the first two harmonics. The amount of rain was well described by the gamma distribution; the shape parameter (gamma) remaining constant but the scale parameter (beta) had a periodic variation which could be represented by a periodic function with two harmonics. Analysis of the data shows that the rainfall series for Piracicaba (1917 to 1944 and 1945 to 1989) can be considered omogeneus...