On the Bayesian estimation and influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

The purpose of this paper is to develop a Bayesian approach for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes and presence of randomized activation mechanisms. We assume the number of competing causes of the event of interest follows a Negative Binomial (NB) distribution while the latent lifetimes are assumed to follow a Weibull distribution. Markov chain Monte Carlos (MCMC) methods are used to develop the Bayesian procedure. Model selection to compare the fitted models is discussed. Moreover, we develop case deletion influence diagnostics for the joint posterior distribution based on the ψ-divergence, which has several divergence measures as particular cases. The developed procedures are illustrated with a real data set.     

An ergonomic analysis of work in the process of professional rehabilitation in Brazil

The purpose of this study is to describe the use of the Ergonomic Analysis of Work (EAW) in the process of rehabilitating workers, insured by the National Institute of Social Security (INSS) in Brazil, and to conduct a brief analysis of the instrument used by this body. Information obtained from EAW enabled the demand, the requirements of the activity and the skills needed to perform the tasks in the workplace to be determined, thus aiding the decision of the INSS as to rehabilitating the workers and their return to their jobs.     

The exponentiated exponential–geometric distribution: a distribution with decreasing,increasing and unimodal failure rate

In this paper, we proposed a new family of distributions namely exponentiated exponential–geometric (E2G) distribution. The E2G distribution is a straightforwardly generalization of the exponential–geometric (EG) distribution proposed by Adamidis and Loukas [A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42], which accommodates increasing, decreasing and unimodal hazard functions. It arises on a latent competing risk scenarios, where the lifetime associated with a particular risk is not observable but only the minimum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments, rth moment of the ith order statistic, mean residual lifetime and modal value. Maximum-likelihood inference is implemented straightforwardly. From a mis-specification simulation study performed in order to assess the extent of the mis-specification errors when testing the EG distribution against the E2G, and we observed that it is usually possible to discriminate between both distributions even for moderate samples with presence of censoring. The practical importance of the new distribution was demonstrated in three applications where we compare the E2G distribution with several lifetime distributions.     

The FGM Long-Term Bivariate Survival Copula Model: Modeling,Bayesian Estimation,and Case Influence Diagnostics

In this article, we propose a bivariate long-term distribution based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo (MCMC) were considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on artificial and real data.     

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.     

Efficient closed-form maximum a posteriori estimators for the gamma distribution

We proposed a new class of maximum a posteriori estimators for the parameters of the Gamma distribution. These estimators have simple closed-form expressions and can be rewritten as a bias-corrected maximum likelihood estimators presented by Ye and Chen [Closed-form estimators for the gamma distribution derived from likelihood equations. Am Statist. 2017;71(2):177–181]. A simulation study was carried out to compare different estimation procedures. Numerical results revels that our new estimation scheme outperforms the existing closed-form estimators and produces extremely efficient estimates for both parameters, even for small sample sizes.     

A log-location-scale lifetime distribution with censored data: Regression modeling,residuals, and global influence

In survival analysis applications, the presence of failure rate functions with non monotone shapes is common. Therefore, models that can accommodate such different shapes are needed. In this article, we present a location regression model based on the complementary exponentiated exponential geometric distribution as an alternative to the usual bathtub, increasing, and decreasing failure rates in lifetime data. Assuming censored data, we consider the maximum likelihood inference for analysis, graphical verification for residuals, and test statistics for influential points.