The log-exponentiated generalized gamma regression model for censored data

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.

General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883-898], proposed a new generalized distribution (denoted here with the prefix 'Kw-G'(Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-Gdensity function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155-161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279-285] and Kw-Flexible Weibull [M. Bebbington, C. D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719-726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Renyi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.

A Bayesian analysis of the Conway-Maxwell-Poisson cure rate model

The purpose of this paper is to develop a Bayesian analysis for the right-censored survival data when immune or cured individuals may be present in the population from which the data is taken. In our approach the number of competing causes of the event of interest follows the Conway-Maxwell-Poisson distribution which generalizes the Poisson distribution. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the proposed model. Also, some discussions on the model selection and an illustration with a real data set are considered.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

Measurement of Direct Photons in Au plus Au Collisions at root s(NN)=200 GeV

We report the measurement of direct photons at midrapidity in Au + Au collisions at root s(NN) = 200 GeV. The direct photon signal was extracted for the transverse momentum range of 4 GeV/c < pT < 22 GeV/c, using a statistical method to subtract decay photons from the inclusive photon sample. The direct photon nuclear modification factor R-AA was calculated as a function of p(T) for different Au + Au collision centralities using the measured p + p direct photon spectrum and compared to theoretical predictions. R-AA was found to be consistent with unity for all centralities over the entire measured pT range. Theoretical models that account for modifications of initial direct photon production due to modified parton distribution functions in Au and the different isospin composition of the nuclei predict a modest change of R-AA from unity. They are consistent with the data. Models with compensating effects of the quark-gluon plasma on high-energy photons, such as suppression of jet-fragmentation photons and induced-photon bremsstrahlung from partons traversing the medium, are also consistent with this measurement.

The McDonald inverted beta distribution

We introduce a five-parameter continuous model, called the McDonald inverted beta distribution, to extend the two-parameter inverted beta distribution and provide new four- and three-parameter sub-models. We give a mathematical treatment of the new distribution including expansions for the density function, moments, generating and quantile functions, mean deviations, entropy and reliability. The model parameters are estimated by maximum likelihood and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A model of road effect using line integrals and a test of the performance of two new road indices using the distribution of small mammals in an Atlantic Forest landscape

Effects of roads on wildlife and its habitat have been measured using metrics, such as the nearest road distance, road density, and effective mesh size. In this work we introduce two new indices: (1) Integral Road Effect (IRE), which measured the sum effects of points in a road at a fixed point in the forest; and (2) Average Value of the Infinitesimal Road Effect (AVIRE), which measured the average of the effects of roads at this point. IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads. Combining tools of ArcGIS software with a numerical algorithm, we calculated these and other road and habitat cover indices in a sample of points in a human-modified landscape in the Brazilian Atlantic Forest, where data on the abundance of two groups of small mammals (forest specialists and habitat generalists) were collected in the field. We then compared through the Akaike Information Criterion (AIC) a set of candidate regression models to explain the variation in small mammal abundance, including models with our two new road indices (AVIRE and IRE) or models with other road effect indices (nearest road distance, mesh size, and road density), and reference models (containing only habitat indices, or only the intercept without the effect of any variable). Compared to other road effect indices, AVIRE showed the best performance to explain abundance of forest specialist species, whereas the nearest road distance obtained the best performance to generalist species. AVIRE and habitat together were included in the best model for both small mammal groups, that is, higher abundance of specialist and generalist small mammals occurred where there is lower average road effect (less AVIRE) and more habitat. Moreover, AVIRE was not significantly correlated with habitat cover of specialists and generalists differing from the other road effect indices, except mesh size, which allows for separating the effect of roads from the effect of habitat on small mammal communities. We suggest that the proposed indices and GIS procedures could also be useful to describe other spatial ecological phenomena, such as edge effect in habitat fragments. (C) 2012 Elsevier B.V. All rights reserved.

An evaluation of dosimetric characteristics of MAGIC gel modified by adding formaldehyde (MAGIC-f)

Purpose: To evaluate the dosimetric characteristics of a new formulation of MAGIC gel, called MAGIC-f, which contains the addition of 3.3% formaldehyde, resulting in a gel with increased thermal stability. Methods: MAGIC-f gel was prepared and stored in hermetically sealed plastic containers. After irradiation, magnetic resonance images (MRI) were acquired to evaluate dose and dose distribution. Dosimetric characterization was performed by means of depth dose measurements, dose response sensitivity and linearity, temporal stability, energy and dose rate dependence, dose integration using sequential beams, temperature influence during MRI acquisition and dose distribution integrity. Results: MAGIC-f depth dose measurements are compatible with the dosimetric table data within +/- 4% uncertainty. The dosimeter's R-2 response varies linearly with dose at least from 0 to 6 Gy. The time-course of the sensitivity of the dosimeter following irradiation, indicated stabilization after 2 weeks. The dosimeter's response to irradiation was altered by 6% when increasing the energy from cobalt beams to 10 MV beams. The dose rate dependence of this new formulation of gel dosimeter is small: less than 2.5% for a variation from 200 to 500 cGy/min, and the dependence with the fractionation scheme is about 50% smaller than for standard MAGIC gel, The dependence on scanning temperature was also verified, and the integrity of the dose distribution was confirmed for a period of 90 days. Conclusions: The results demonstrate the applicability of this new dosimeter in tridimensional dose distribution measurements. (C) 2012 Elsevier Ltd. All rights reserved.

Mechanistic changes observed in heavy water for nitrate reduction reaction on palladium-modified Pt(hkl) electrodes

Reduction of nitrate on palladium-modified platinum single-crystal electrodes has been investigated both voltammetrically and spectroscopically in acidic media (pH = 1). Results obtained in H2O and D2O solvents are compared for the three crystallographic orientations. FTIR and differential electrochemical mass spectrometry (DEMS) results clearly indicate that the isotopic substitution of the solvent has a large effect in the mechanism of the reaction, changing the nature of the detected products. For Pt(111)/Pd and Pt(100)/Pd, N2O is detected as the main product of nitrate reduction when D2O is used as solvent, while no N2O is detected when the reaction is performed in H2O. For Pt(110)/Pd, N2O is detected in both solvents, although the use of D2O clearly favours the preferential formation of this product. The magnitude of voltammetric currents is also affected by the nature of the solvent. This has been analysed considering, in addition to the different product distribution, the existence of different transport numbers and optical constants of the solvent.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.