The Kumaraswamy Gumbel distribution

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

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.

Endothelial function in pre-pubertal children at risk of developing cardiomyopathy: a new frontier

Although it is known that obesity, diabetes, and Kawasaki's disease play important roles in systemic inflammation and in the development of both endothelial dysfunction and cardiomyopathy, there is a lack of data regarding the endothelial function of pre-pubertal children suffering from cardiomyopathy. In this study, we performed a systematic review of the literature on pre-pubertal children at risk of developing cardiomyopathy to assess the endothelial function of pre-pubertal children at risk of developing cardiomyopathy. We searched the published literature indexed in PubMed, Bireme and SciELO using the keywords 'endothelial', 'children', 'pediatric' and 'infant' and then compiled a systematic review. The end points were age, the pubertal stage, sex differences, the method used for the endothelial evaluation and the endothelial values themselves. No studies on children with cardiomyopathy were found. Only 11 papers were selected for our complete analysis, where these included reports on the flow-mediated percentage dilatation, the values of which were 9.80±1.80, 5.90±1.29, 4.50±0.70, and 7.10±1.27 for healthy, obese, diabetic and pre-pubertal children with Kawasaki's disease, respectively. There was no significant difference in the dilatation, independent of the endothelium, either among the groups or between the genders for both of the measurements in children; similar results have been found in adolescents and adults. The endothelial function in cardiomyopathic children remains unclear because of the lack of data; nevertheless, the known dysfunctions in children with obesity, type 1 diabetes and Kawasaki's disease may influence the severity of the cardiovascular symptoms, the prognosis, and the mortality rate. The results of this study encourage future research into the consequences of endothelial dysfunction in pre-pubertal children.

Common bile duct stones: analysis of the videolaparoscopic surgical treatment

CONTEXT: About 9% of the Brazilian population has gallstones and the incidence increases significantly with aging. The choledocholithiasis is found around 15% of these patients, and a third to half of these cases presented as asymptomatic. Once the lithiasis in the common bile duct is characterized through intraoperative cholangiography, the laparoscopic surgical exploration can be done through the transcystic way or directly through choledochotomy. OBJECTIVE: To evaluate the results and outcomes of the laparoscopic treatment of common bile duct lithiasis. METHODS: Seventy consecutive patients were evaluated. They prospectively underwent the treatment of the lithiasis in the common bile duct and the exploration ways were compared according to the following parameters: criteria on their indication, success in the clearance, surgical complications. It was verified that about ½ of the choledocholithiasis carriers did not show any expression of predictive factors (clinical antecedents of jaundice and/or acute pancreatitis, compatible sonographic data and the pertaining lab tests). The laparoscopic exploration through the transcystic way is favored when there are no criteria for the practice of primary choledochotomy, which are: lithiasis in the proximal bile duct, large (over 8 mm) or numerous calculi (multiple calculosis). RESULTS: The transcystic way was employed in about 50% of the casuistic and the choledochotomy in about 30%. A high success rate (around 80%) was achieved in the clearance of the common bile duct stones through laparoscopic exploration. The transcystic way, performed without fluoroscopy or choledochoscopy, attained a low rate of success (around 45%), being 10% of those by transpapilar pushing of calculi less than 3 mm. The exploration through choledochotomy, either primary or secondary, if the latter was performed after the transcystic route failure, showed high success rate (around 95%). When the indication to choledochotomy was primary, the necessity for choledochoscopy through choledochotomy to help in the removal of the calculi was 55%. However, when choledochotomy was performed secondarily, in situations where the common bile duct diameter was larger than 6 mm, the use of choledochoscopy with the same purpose involved about 20% of the cases. There was no mortality in this series. CONCLUSION: The laparoscopic exploration of the common bile duct was related to a low rate of morbidity. Therefore, the use of laparoscopy for the treatment of the lithiasis in the common bile duct depends on the criteria for the choice of the best access, making it a safe procedure with very good results.

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.

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.

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.

Benthic foraminiferal distribution on the southeastern Brazilian shelf and upper slope

Foraminiferal data were obtained from 66 samples of box cores on the southeastern Brazilian upper margin (between 23.8A degrees-25.9A degrees S and 42.8A degrees-46.13A degrees W) to evaluate the benthic foraminiferal fauna distribution and its relation to some selected abiotic parameters. We focused on areas with different primary production regimes on the southern Brazilian margin, which is generally considered as an oligotrophic region. The total density (D), richness (R), mean diversity (H) over bar`, average living depth (ALD(X) ) and percentages of specimens of different microhabitats (epifauna, shallow infauna, intermediate infauna and deep infauna) were analyzed. The dominant species identified were Uvigerina spp., Globocassidulina subglobosa, Bulimina marginata, Adercotryma wrighti, Islandiella norcrossi, Rhizammina spp. and Brizalina sp.. We also established a set of mathematical functions for analyzing the vertical foraminiferal distribution patterns, providing a quantitative tool that allows correlating the microfaunal density distributions with abiotic factors. In general, the cores that fit with pure exponential decaying functions were related to the oligotrophic conditions prevalent on the Brazilian margin and to the flow of the Brazilian Current (BC). Different foraminiferal responses were identified in cores located in higher productivity zones, such as the northern and the southern region of the study area, where high percentages of infauna were encountered in these cores, and the functions used to fit these profiles differ appreciably from a pure exponential function, as a response of the significant living fauna in deeper layers of the sediment. One of the main factors supporting the different foraminiferal assemblage responses may be related to the differences in primary productivity of the water column and, consequently, in the estimated carbon flux to the sea floor. Nevertheless, also bottom water velocities, substrate type and water depth need to be considered.

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.

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 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 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.

Nuclear Factor (NF) κB polymorphism is associated with heart function in patients with heart failure

Abstract Background Cardiac remodeling is generally an adverse sign and is associated with heart failure (HF) progression. NFkB, an important transcription factor involved in many cell survival pathways, has been implicated in the remodeling process, but its role in the heart is still controversial. Recently, a promoter polymorphism associated with a lesser activation of the NFKB1 gene was also associated with Dilated Cardiomyopathy. The purpose of this study was to evaluate the association of this polymorphism with clinical and functional characteristics of heart failure patients of different etiologies. Methods A total of 493 patients with HF and 916 individuals from a cohort of individuals from the general population were investigated. The NFKB1 -94 insertion/deletion ATTG polymorphism was genotyped by High Resolution Melt discrimination. Allele and genotype frequencies were compared between groups. In addition, frequencies or mean values of different phenotypes associated with cardiovascular disease were compared between genotype groups. Finally, patients were prospectively followed-up for death incidence and genotypes for the polymorphism were compared regarding disease onset and mortality incidence in HF patients. Results We did not find differences in genotype and allelic frequencies between cases and controls. Interestingly, we found an association between the ATTG1/ATTG1 genotype with right ventricle diameter (P = 0.001), left ventricle diastolic diameter (P = 0.04), and ejection fraction (EF) (P = 0.016), being the genotype ATTG1/ATTG1 more frequent in patients with EF lower than 50% (P = 0.01). Finally, we observed a significantly earlier disease onset in ATTG1/ATTG1 carriers. Conclusion There is no genotype or allelic association between the studied polymorphism and the occurrence of HF in the tested population. However, our data suggest that a diminished activation of NFKB1, previously associated with the ATTG1/ATTG1 genotype, may act modulating on the onset of disease and, once the individual has HF, the genotype may modulate disease severity by increasing cardiac remodeling and function deterioration.