The exponentiated generalized gamma distribution with application to lifetime data

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.

The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Deviance residuals in generalised log-gamma regression models with censored observations

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.

The exponentiated generalized inverse Gaussian distribution

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.

Variabilidade amostral das séries mensais de precipitação pluvial em duas regiões do Brasil: Pelotas-RS e Campinas-SP

O presente trabalho avaliou a variabilidade amostral dos parâmetros da distribuição gama, relativos a séries mensais de precipitação pluvial, nas regiões de Campinas-SP e Pelotas-RS, que têm dados para os períodos de 1890-2006 e 1890-2005, respectivamente. Assim, os espaços amostrais considerados foram de 58, 39 e 29 anos para Campinas e 58 e 29 anos para Pelotas. As análises foram feitas usando o teste da razão da máxima verossimilhança. Os resultados apontaram significativas alterações amostrais. Não houve indicações de tendências contínuas (redução ou aumento) no regime mensal de precipitação pluvial na região de Campinas-SP. Em contrapartida, esse teste indicou, para a localidade de Pelotas-RS, tendência de elevação no regime desse elemento meteorológico ocorrida entre as amostras relativas aos anos de 1948 a 1976 e 1977 a 2005.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Gamma Knife(A (R)) 3-D Dose Distribution Mapping by Magnetic Resonance Imaging

In medical processes where ionizing radiation is used, dose planning and dose delivery are the key elements to patient safety and treatment success, particularly, when the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Therefore, the radiation dose should be well defined and precisely delivered to the target while minimizing radiation exposure to surrounding normal tissues [1]. Several methods have been proposed to obtain three-dimensional (3-D) dose distribution [2, 3]. In this paper, we propose an alternative method, which can be easily implemented in any stereotactic radiosurgery center with a magnetic resonance imaging (MRI) facility. A phantom with or without scattering centers filled with Fricke gel solution is irradiated with Gamma Knife(A (R)) system at a chosen spot. The phantom can be a replica of a human organ such as head, breast or any other organ. It can even be constructed from a real 3-D MR image of an organ of a patient using a computer-aided construction and irradiated at a specific region corresponding to the tumor position determined by MRI. The spin-lattice relaxation time T (1) of different parts of the irradiated phantom is determined by localized spectroscopy. The T (1)-weighted phantom images are used to correlate the image pixels intensity to the absorbed dose and consequently a 3-D dose distribution with a high resolution is obtained.

Methodological analysis of gamma tomography system for large random packed columns

Gamma ray tomography experiments have been carried out to detect spatial patterns in the porosity in a 0.27 m diameter column packed with steel Rashig rings of different sizes: 12.6, 37.9, and 76 mm. using a first generation CT system (Chen et al., 1998). A fast Fourier transform tomographic reconstruction algorithm has been used to calculate the spatial variation over the column cross section. Cross-sectional gas porosity and solid holdup distribution were determinate. The values of cross-sectional average gas porosity were epsilon=0.849, 0.938 and 0.966 for the 12.6, 37.9, and 76 mm rings, respectively. Radial holdup variation within the packed bed has been determined. The variation of the circumferentially averaged gas holdup in the radial direction indicates that the porosity in the column wall region is a somewhat higher than that in the bulk region, due to the effect of the column wall. (C) 2009 Elsevier Ltd. All rights reserved.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

Quality control of blood irradiation with a teletherapy unit: damage to stored red blood cells after cobalt-60 gamma irradiation

BACKGROUND: Previous publications have documented the damage caused to red blood cells (RBCs) irradiated with X-rays produced by a linear accelerator and with gamma rays derived from a Cs-137 source. The biologic effects on RBCs of gamma rays from a Co-60 source, however, have not been characterized. STUDY DESIGN AND METHODS: This study investigated the effect of 3000 and 4000 cGy on the in vitro properties of RBCs preserved with preservative solution and irradiated with a cobalt teletherapy unit. A thermal device equipped with a data acquisition system was used to maintain and monitor the blood temperature during irradiation. The device was rotated at 2 r.p.m. in the irradiation beam by means of an automated system. The spatial distribution of the absorbed dose over the irradiated volume was obtained with phantom and thermoluminescent dosimeters (TLDs). Levels of Hb, K+, and Cl- were assessed by spectrophotometric techniques over a period of 45 days. The change in the topology of the RBC membrane was investigated by flow cytometry. RESULTS: Irradiation caused significant changes in the extracellular levels of K+ and Hb and in the organizational structure of the phospholipid bilayer of the RBC membrane. Blood temperature ranged from 2 to 4 degrees C during irradiation. Rotation at 2 r.p.m. distributed the dose homogeneously (92%-104%) and did not damage the RBCs. CONCLUSIONS: The method used to store the blood bags during irradiation guaranteed that all damage caused to the cells was exclusively due to the action of radiation at the doses applied. It was demonstrated that prolonged storage of Co-60-irradiated RBCs results in loss of membrane phospholipids asymmetry, exposing phosphatidylserine (PS) on the cells` surface with a time and dose dependence, which can reduce the in vivo recovery of these cells. A time- and dose-dependence effect on the extracellular K+ and plasma-free Hb levels was also observed. The magnitude of all these effects, however, seems not to be clinically important and can support the storage of irradiated RBC units for at last 28 days.

Study of the spatial distribution of the absorbed dose in blood volumes irradiated using a teletherapy unit

Blood irradiation can be performed using a dedicated blood irradiator or a teletherapy unit. A thermal device providing appropriate storage conditions during blood components irradiation with a teletherapy unit has been recently proposed. However, the most appropriated volume of the thermal device was not indicated. The goal of this study was to indicate the most appropriated blood volume for irradiation using a teletherapy unit in order to minimize both the dose heterogeneity in the volume and the blood irradiation time using these equipments. Theoretical and experimental methods were used to study the dose distribution in the blood volume irradiated using a linear accelerator and a cobalt-60 therapy machine. The calculation of absorbed doses in the middle plane of cylindrical acrylic volumes was accomplished by a treatment planning system. Experimentally, we also used cylindrical acrylic phantoms and thermoluminescent dosimeters to confirm the calculated doses. The data obtained were represented by isodose curves. We observed that an irradiation volume should have a height of 28 cm and a diameter of 28 cm and a height of 35 cm and a diameter of 35 cm, when the irradiation is to be performed by a linear accelerator and a cobalt-60 teletherapy unit, respectively. Calculated values of relative doses varied from 93% to 100% in the smaller volume, and from 66% to 100% in the largest one. A difference of 5.0%, approximately, was observed between calculated and experimental data. The size of these volumes permits the irradiation of blood bags in only one bath without compromising the homogeneity of the absorbed dose over the irradiated volume. Thus, these irradiation volumes can be recommend to minimize the irradiation time when a teletherapy unit is used to irradiate blood. (C) 2010 Elsevier Ltd. All rights reserved.

Haplotypes of the bovine IgG2 heavy gamma chain in tick-resistant and tick-susceptible breeds of cattle

Bovines present contrasting, heritable phenotypes of infestations with the cattle tick, Rhipicephalus (Boophilus) microplus. Tick salivary glands produce IgG-binding proteins (IGBPs) as a mechanism for escaping from host antibodies that these ectoparasites ingest during blood meals. Allotypes that occur in the constant region of IgG may differ in their capacity to bind with tick IGBPs; this may be reflected by the distribution of distinct allotypes according to phenotypes of tick infestations. In order to test this hypothesis, we investigated the frequency of haplotypes of bovine IgG2 among tick-resistant and tick-susceptible breeds of bovines. Sequencing of the gene coding for the heavy chain of IgG2 from 114 tick-resistant (Bos taurus indicus, Nelore breed) and tick-susceptible (B. t. taurus, Holstein breed) bovines revealed SNPs that generated 13 different haplotypes, of which 11 were novel and 5 were exclusive of Holstein and 3 of Nelore breeds. Alignment and modeling of coded haplotypes for hinge regions of the bovine IgG2 showed that they differ in the distribution of polar and hydrophobic amino acids and in shape according to the distribution of these amino acids. We also found that there was an association between genotypes of the constant region of the IgG2 heavy chain with phenotypes of tick infestations. These findings open the possibility of investigating if certain IgG allotypes hinder the function of tick IGBPs. If so, they may be markers for breeding for resistance against tick infestations.

Effects of 15-deoxy-Delta(12, 14) prostaglandin J(2) and ciglitazone on human cancer cell cycle progression and death: The role of PPAR gamma

The role of PPAR-gamma in ciglitazone and 15-d PGJ(2)-induced apoptosis and cell cycle arrest of Jurkat (before and after PPAR gamma gene silencing), U937 (express high levels of PPAR gamma) and HeLa (that express very low levels of PPAR gamma) cells was investigated. PPAR gamma gene silencing, per se, induced a G2/M cell arrest, loss of membrane integrity and DNA fragmentation of Jurkat cells, indicating that PPAR gamma is important for this cell survival and proliferation. Ciglitazone-induced apoptosis was abolished after knockdown of PPAR gamma suggesting a PPAR gamma-dependent pro-apoptotic effect. However, ciglitazone treatment was toxic for U937 and HeLa cells regardless of the presence of PPAR gamma. This treatment did not change the cell cycle distribution corroborating with a PPAR gamma-independent mechanism. On the other hand, 15-d PGJ(2) induced apoptosis of the three cancer cell lines regardless of the expression of PPAR gamma. These results suggest that PPAR gamma plays an important role for death of malignant T lymphocytes (Jurkat cells) and PPAR gamma agonists exert their effects through PPAR gamma-dependent and -independent mechanisms depending on the drug and the cell type. (C) 2007 Elsevier B.V. All rights reserved.