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.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive 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.

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.

The Poisson-exponential regression model under different latent activation schemes

In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activation schemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer.

Lifetime Prevalence, Age and Gender Distribution and Age-of-Onset of Psychiatric Disorders in the Sao Paulo Metropolitan Area, Brazil: Results from the Sao Paulo Megacity Mental Health Survey

Objectives: To estimate prevalence, age-of-onset, gender distribution and identify correlates of lifetime psychiatric disorders in the Sao Paulo Metropolitan Area (SPMA). Methods: The Sao Paulo Megacity Mental Health Survey assessed psychiatric disorders on a probabilistic sample of 5,037 adult residents in the SPMA, using the World Mental Health Survey Version of the Composite International Diagnostic Interview. Response rate was 81.3%. Results: Lifetime prevalence for any disorder was 44.8%; estimated risk at age 75 was 57.7%; comorbidity was frequent. Major depression, specific phobias and alcohol abuse were the most prevalent across disorders; anxiety disorders were the most frequent class. Early age-of-onset for phobic and impulse-control disorders and later age-of-onset for mood disorders were observed. Women were more likely to have anxiety and mood disorders, whereas men, substance use disorders. Apart from conduct disorders, more frequent in men, there were no gender differences in impulse-control disorders. There was a consistent trend of higher prevalence in the youngest cohorts. Low education level was associated to substance use disorders. Conclusions: Psychiatric disorders are highly prevalent among the general adult population in the SPMA, with frequent comorbidity, early age-of-onset for most disorders, and younger cohorts presenting higher rates of morbidity. Such scenario calls for vigorous public health action.

Mapping the lignin distribution in pretreated sugarcane bagasse by confocal and fluorescence lifetime imaging microscopy

Abstract Background Delignification pretreatments of biomass and methods to assess their efficacy are crucial for biomass-to-biofuels research and technology. Here, we applied confocal and fluorescence lifetime imaging microscopy (FLIM) using one- and two-photon excitation to map the lignin distribution within bagasse fibers pretreated with acid and alkali. The evaluated spectra and decay times are correlated with previously calculated lignin fractions. We have also investigated the influence of the pretreatment on the lignin distribution in the cell wall by analyzing the changes in the fluorescence characteristics using two-photon excitation. Eucalyptus fibers were also analyzed for comparison. Results Fluorescence spectra and variations of the decay time correlate well with the delignification yield and the lignin distribution. The decay dependences are considered two-exponential, one with a rapid (τ1) and the other with a slow (τ2) decay time. The fastest decay is associated to concentrated lignin in the bagasse and has a low sensitivity to the treatment. The fluorescence decay time became longer with the increase of the alkali concentration used in the treatment, which corresponds to lignin emission in a less concentrated environment. In addition, the two-photon fluorescence spectrum is very sensitive to lignin content and accumulation in the cell wall, broadening with the acid pretreatment and narrowing with the alkali one. Heterogeneity of the pretreated cell wall was observed. Conclusions Our results reveal lignin domains with different concentration levels. The acid pretreatment caused a disorder in the arrangement of lignin and its accumulation in the external border of the cell wall. The alkali pretreatment efficiently removed lignin from the middle of the bagasse fibers, but was less effective in its removal from their surfaces. Our results evidenced a strong correlation between the decay times of the lignin fluorescence and its distribution within the cell wall. A new variety of lignin fluorescence states were accessed by two-photon excitation, which allowed an even broader, but complementary, optical characterization of lignocellulosic materials. These results suggest that the lignin arrangement in untreated bagasse fiber is based on a well-organized nanoenvironment that favors a very low level of interaction between the molecules.

Lifetime Prevalence, age and gender distribution and age-of-onset of psychiatric disorders in the São Paulo Metropolitan Area, Brazil: results from the São Paulo Megacity Mental Health Survey

OBJECTIVES: To estimate prevalence, age-of-onset, gender distribution and identify correlates of lifetime psychiatric disorders in the São Paulo Metropolitan Area (SPMA). METHODS: The São Paulo Megacity Mental Health Survey assessed psychiatric disorders on a probabilistic sample of 5,037 adult residents in the SPMA, using the World Mental Health Survey Version of the Composite International Diagnostic Interview. Response rate was 81.3%. RESULTS: Lifetime prevalence for any disorder was 44.8%; estimated risk at age 75 was 57.7%; comorbidity was frequent. Major depression, specific phobias and alcohol abuse were the most prevalent across disorders; anxiety disorders were the most frequent class. Early age-of-onset for phobic and impulse-control disorders and later age-of-onset for mood disorders were observed. Women were more likely to have anxiety and mood disorders, whereas men, substance use disorders. Apart from conduct disorders, more frequent in men, there were no gender differences in impulse-control disorders. There was a consistent trend of higher prevalence in the youngest cohorts. Low education level was associated to substance use disorders. CONCLUSIONS: Psychiatric disorders are highly prevalent among the general adult population in the SPMA, with frequent comorbidity, early age-of-onset for most disorders, and younger cohorts presenting higher rates of morbidity. Such scenario calls for vigorous public health action.

An extended Lindley distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

A general threshold stress hybrid hazard model for lifetime data

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.

Subcritical crack growth and in vitro lifetime prediction of resin composites with different filler distributions

Objectives. Verify the influence of different filler distributions on the subcritical crack growth (SCG) susceptibility, Weibull parameters (m and sigma(0)) and longevity estimated by the strength-probability-time (SPT) diagram of experimental resin composites. Methods. Four composites were prepared, each one containing 59 vol% of glass powder with different filler sizes (d(50) = 0.5; 0.9; 1.2 and 1.9 mu m) and distributions. Granulometric analyses of glass powders were done by a laser diffraction particle size analyzer (Sald-7001, Shimadzu, USA). SCG parameters (n and sigma(f0)) were determined by dynamic fatigue (10(-2) to 10(2) MPa/s) using a biaxial flexural device (12 x 1.2 mm; n = 10). Twenty extra specimens of each composite were tested at 10(0) MPa/s to determine m and sigma(0). Specimens were stored in water at 37 degrees C for 24 h. Fracture surfaces were analyzed under SEM. Results. In general, the composites with broader filler distribution (C0.5 and C1.9) presented better results in terms of SCG susceptibility and longevity. C0.5 and C1.9 presented higher n values (respectively, 31.2 +/- 6.2(a) and 34.7 +/- 7.4(a)). C1.2 (166.42 +/- 0.01(a)) showed the highest and C0.5 (158.40 +/- 0.02(d)) the lowest sigma(f0) value (in MPa). Weibull parameters did not vary significantly (m: 6.6 to 10.6 and sigma(0): 170.6 to 176.4 MPa). Predicted reductions in failure stress (P-f = 5%) for a lifetime of 10 years were approximately 45% for C0.5 and C1.9 and 65% for C0.9 and C1.2. Crack propagation occurred through the polymeric matrix around the fillers and all the fracture surfaces showed brittle fracture features. Significance. Composites with broader granulometric distribution showed higher resistance to SCG and, consequently, higher longevity in vitro. (C) 2012 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

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 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.