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...

In this paper we introduce a four-parameter generalized Weibull distribution. This new distribution has a more general form of failure rate function. It is more general for modeling than six ageing classes of life distributions with appropriate choices of parameter values, so it can display decreasing, increasing, bathtub shaped, unimodal, increasing-decreasing increasing and decreasing-increas...

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the mode...

A five-parameter distribution called Beta Generalized Weibull (BGW) distribution is introduced. Beta Generalized Exponential (BGE), Beta Weibull (BW), Generalized or Exponentiated Weibull (GW or EW), Generalized Rayleigh (GR), Beta Exponential (BE), Generalized Exponential (GE), Weibull, Rayleigh and Exponential are its sub models. The cumulative distribution function (cdf) and the probability ...

investigation of reliability characteristics under fuzzy environments is proposed in this paper. fuzzy weibull distribution and lifetimes of components are using it described. formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. finally, some numeric...

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...

In this talk we review several applications of two Weibull extensions in statistical theory and applied research. The two extensions are the generalized Weibull and the exponentiated Weibull families, and the applications are in the areas of reliability and survival analysis, exteme value analysis, isotones and distributional approximations. 1 The Generalized Weibull Family The generalized Weib...

  Spreading and coating of nano and micro droplets on solid surfaces is important in a wide variety of applications including plasma spray coating, ink jet printing, DNA synthesis and etc. In spraying processes, most of droplets collide obliquely to the surface. The purpose of this article is to study the distribution of nano and micro droplets spreading when droplets impact at an oblique a...

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture strength of brittle materials, maximal annual rainfall, wind speed and earthquake return times. We investiga...