The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

A frailty modeling approach for parental effects in animal breeding

Survival models involving frailties are commonly applied in studies where correlated event time data arise due to natural or artificial clustering. In this paper we present an application of such models in the animal breeding field. Specifically, a mixed survival model with a multivariate correlated frailty term is proposed for the analysis of data from over 3611 Brazilian Nellore cattle. The primary aim is to evaluate parental genetic effects on the trait length in days that their progeny need to gain a commercially specified standard weight gain. This trait is not measured directly but can be estimated from growth data. Results point to the importance of genetic effects and suggest that these models constitute a valuable data analysis tool for beef cattle breeding.

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.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved