In this article, a new family of lifetime distributions by adding an additional parameter to the existing distributions is introduced. The new family is called, the extended alpha power transformed family of distributions. For the proposed family, explicit expressions for some mathematical properties along with estimation of parameters through Maximum likelihood Method are discussed. A special sub-model, called the extended alpha power transformed Weibull distribution is considered in detail. The proposed model is very flexible and can be used to model data with increasing, decreasing or bathtub shaped hazard rates. To access the behavior of the model parameters, a small simulation study has also been carried out. For the new family, some useful characterizations are also presented. Finally, the potentiality of the proposed method is showen via analyzing two real data sets taken from reliability engineering and bio-medical fields.
Abstract: In recent years, many modifications of the Weibull distribution have been proposed. Some of these modifications have a large number of parameters and so their real benefits over simpler modifications are questionable. Here, we use two data sets with modified unimodal (unimodal followed by increasing) hazard function for comparing the exponentiated Weibull and generalized modified Weibull distributions. We find no evidence that the generalized modified Weibull distribution can provide a better fit than the exponentiated Weibull distribution for data sets exhibiting the modified unimodal hazard function.In a related issue, we consider Carrasco et al. (2008), a widely cited paper, proposing the generalized modified Weibull distribution, and illustrating two real data applications. We point out that some of the results in both real data applications in Carrasco et al. (2008) 1 are incorrect.
Abstract: The Weibull distribution has received much interest in reliability theory. The well-known maximum likelihood estimators (MLE) of this fam ily are not available in closed form expression. In this work, we propose a consistent and closed form estimator for shape parameter of three-parameter Weibull distribution. Apart from high degree of performance, the derived estimator is location and scale-invariant.
In this paper, we introduce a new four-parameter distribution called the transmuted Weibull power function (TWPF) distribution which e5xtends the transmuted family proposed by Shaw and Buckley . The hazard rate function of the TWPF distribution can be constant, increasing, decreasing, unimodal, upside down bathtub shaped or bathtub shape. Some mathematical properties are derived including quantile functions, expansion of density function, moments, moment generating function, residual life function, reversed residual life function, mean deviation, inequality measures. The estimation of the model parameters is carried out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using real data sets.
In this paper, maximum likelihood and Bayesian methods of estimation are used to estimate the unknown parameters of two Weibull populations with the same shape parameter under joint progressive Type-I (JPT-I) censoring scheme. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. The approximate confidence intervals and the credible intervals for the unknown parameters are also obtained. Finally, we analyze a one real data set for illustration purpose.