Distributions of parameters What are the traditional distributions for assigning probabilities to model parameters?
For instance, assume that we have a binomial distribution:
$$y \sim Bin(n,\theta)$$
Then we can distribute $\theta$ parameter with a Beta distribution and parameters $\alpha$ and $\beta$ equal to 1. 
$$\theta \sim Beta(1,1)$$
I consider that if we would like to derive the distribution of the mean of a Gaussian probability distribution, then we could use the central limit theorem and assume that:
$$\mu \sim N(0,1)$$
But what about other distributions? For instance, what is the distribution of $\lambda$ in the Weibull distribution? Or what is the distribution of $k$ for Chi-squared distribution? I'm not sure where to find papers on this topic because in most cases the usage of techniques involving parameters distributions seems like more of an intuitive methodology than some kind of rule.
Update: 
I'm asking this question for the Bayesian parameters estimation and Bayesian model selection, where I calculate posterior with:
$$P(\theta|y) = P(y|\theta)P(\theta)$$
So I need to find the prior $P(\theta)$, that's what I was interested in.
 A: You seem to be asking for the distribution to model certain parameters. However, there is no single distribution for certain types of parameters. There are common distributions used for parameters such as the Beta distribution to model a probability. No matter how common they are, they may not be the most accurate distribution to describe your problem. Oftentimes, the "common" distributions for parameters are common due to convenience of some sort. Either they're conjugate or have other nice mathematics associated with them.
I would caution against using these distributions just for convenience sake as there oftentimes better distributions for your task. For example, the Beta distribution cannot be made to be trimodal. If you're modeling probabilities that you think must be in a neighborhood of 0.0, 0.5, or 1.0 this may not be sufficient. Another example is the Normal distibrution as a prior, which has really small mass in extreme values. Oftentimes, these extreme values aren't really as implausible as your Normal prior is suggesting (t-distribution is a good alternative). If you want to really put good priors on your parameters, you're going to have think about your problem and think about what makes sense and not just simply go with what's common. 
Now, there are good reasons to go with the common distributions for reasons other than they most accurately describe your problem. It's entirely possible that you may have to make some sacrifices for computational or numerical efficiency, but to default to these types of "common" distributions I think is misguided.
