A statistical parameter is a quantity that indexes a family of probability distributions.
Wikipedia has the following definition of a shape parameter:
A shape parameter is any parameter of a probability distribution that is neither a location parameter nor a scale parameter (nor a function of either or both of these only, such as a rate parameter). Such a parameter must affect the shape of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does).
Therefore we have only four types (classes/categories) of parameters of a parametric family:
- location parameters
- scale parameters
- shape parameters
- functions of location and/or scale (such as rate parameter = $\frac{1}{\text{scale}}$)
If so I have the following questions:
What is the type of parameters which we call "degrees of freedom" (for example, parameter $k$ of the Chi-squared distribution $\chi^2(k)$) ?
What is the type of parameters $n$ and $p$ of the Binomial distribution $\mathrm{Bin}(n,p)$ ?
