Use of Weibull model or Weibull distribution I have a basic question regarding use of the terms "Weibull model" and "Weibull distribution". (I take Weibull as an example, but the question could apply to any distribution.) 
I read in books or research papers frequent use of "Weibull model" or "Weibull distribution", so my questions are
1) Are the meanings of Weibull model and Weibull distribution the same? 
2) If not so, in what situations do we use Weibull model or Weibull distribution?
 A: The Weibull distribution may be used to model a single random variable, for example time to failure in engineering. 
If there are many variables contributing to time to failure, then a multivariate Weibull model can be constructed where the expected value of the scale or shape parameter is dependent upon a linear combination of variables. Using a log link for either parameter is useful given that the scale and shape parameters must be > 0.
A: I think this is largely about terminology and how it is used. 
A short answer is that there is no very hard and fast distinction, and in practice usages overlap or intergrade. 
It might be a bit more common to talk about fitting a Weibull distribution when the problem was univariate, i.e. we have just one variable and we fit such a distribution to it. 
As the statistical problem gets more complex and (in particular) we have not just a response or dependent variable, but also predictors or independent variables, so that the Weibull of concern is a distribution conditional on predictors, then it would be much more common to talk about Weibull modelling. 
I'd also see "Weibull modelling" as being the wider term, which includes fitting Weibull distributions. There are some circles in which the use of "modelling" just for fitting univariate distributions might be regarded as pretentious, but that is more sociology than statistics. 
Checking with other examples, I feel equally comfortable talking about fitting a Poisson model and fitting a Poisson distribution. But "Poisson modelling" could easily be much broader than just univariate distribution fitting. 
A: A distribution assigns probabilities to events. For example, the standard normal distribution with density $\mathcal{N}_{0, 1}(x)$ assigns every event $\left[a, b\right]$ the probability
$$\int_a^b \mathcal{N}_{0, 1}(x) \, dx.$$
Statistical models are families of probability distributions. An example of a parametric model  would be a set of Gaussian distributions,
$$\left\{\mathcal{N}_{\mu, \sigma^2} : \mu \in \mathbb{R}, \sigma^2 \in \left]0, \infty\right[\right\}.$$
I imagine the terminology is no different for the Weibull distribution. However, in practice, "distribution" and "model" are often used sloppily and interchangeably.
