No abstract

The Weibull distribution has prominent applications in the engineering sector. However, due to its monotonic behavior of the hazard function, the Weibull model does not provide the best fit for data in many cases. This paper introduces a new family of distributions to obtain new flexible distributions. The proposed family is called a novel generalized- M family. Based on this approach, an updated version of the Weibull distribution is introduced. The updated version of the Weibull distribution is called a novel generalized Weibull distribution. The proposed distribution is able to capture four different patterns of the hazard function. Some mathematical properties of the proposed method are obtained. Furthermore, the maximum likelihood estimators of the proposed family are also obtained. Moreover, a simulation study is conducted for evaluating these estimators. For illustrating the proposed model, two data sets from the engineering sector are analyzed. Based on some well-known analytical measures, it is shown that the novel generalized Weibull distribution is the best competing distribution for analyzing the engineering data sets.

The study of system safety and reliability has always been vital for the quality and manufacturing engineers of varying fields for which generally the continuous probability distributions are proposed. Bivariate and multivariate continuous distributions are the candidates while studying more than one characteristic of the system. In this article, an attempt is made to address this issue when the reliability systems generate bivariate and correlated count datasets. The bivariate generalized geometric distribution (BGGD) is believed to serve as a potential candidate to model such types of datasets. Bayesian approach of data analysis has the potential of accommodating the uncertainty associated with the model parameters of interest using uninformative and informative priors. A real life bivariate correlated dataset is analyzed in Bayesian framework and the results are compared with those produced by the classical approach. Posterior summaries including posterior means, highest density regions, and predicted expected frequencies of the bivariate data are evaluated. Different information criteria are evaluated to compare the inferential methods under study. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) set-up of data augmentation implemented through WinBUGS.