In this paper we consider the Marshall-Olkin bivariate Weibull distribution. The Marshall-Olkin bivariate Weibull distribution is a singular distribution, whose both the marginals are univariate Weibull distributions. This is a generalization of the Marshall-Olkin bivariate exponential distribution. The cumulative joint distribution of the Marshall-Olkin bivariate Weibull distribution is a mixt...

Weibull mixtures have been used extensively in reliability and survival analysis, and they have also been generalized by allowing negative mixing weights, which arise naturally under the formation of some structures of reliability systems. These models provide exible distributions for modelling dependent lifetimes from heterogeneous populations. In this paper, we study conditions on the mixing ...

We propose the Weibull negative binomial distribution that is a quite flexible model to analyze positive data, and includes as special submodels the Weibull, Weibull Poisson and Weibull geometric distributions. Some of its structural properties follow from the fact that its density function can be expressed as a mixture of Weibull densities. We provide explicit expressions for moments, generati...

A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are...

In this article, the failure rates of the system's components are functions of time t. We study two cases (i) the mixture of two stages of life time distribution with Weibull failure rates, (ii) the mixture of two stages failure rates with Weibull distribution. The reliability equivalence factors of some systems with identical components are obtained. Two different methods are used to improve t...

The cumulative leukemia-free survival rate of refractory anemia with excess of blasts was fitted to three parametric failure time models, i.e., the usual exponential and Weibull, and exponential mixture models. Among the three, the best fit model was the exponential mixture model, which was 119 times more likely to assume that samples came from the exponential mixture distribution than to assum...

A finite mixture model is used to describe the diameter distributions of mixed-species forest stands. A three-parameter Weibull function is assumed as the component probability density function in the finite mixture model. Four example plots, each with two species, are selected to demonstrate model fitting and comparison. It appears that the finite mixture model is flexible enough to fit irregu...