I am reviewing Fisher information and saw that one of the requirements is that the distribution of the data, say $f(x|\theta)$, involves a parameter $\theta$ that is unknown but lies within a given open interval $\Omega$ of the real line.
Does the mean that if I have a distribution where the parameter is the natural numbers I cannot calculate Fisher's Information?
For example:
- Hypergeometric distribution
- Chi-square with $k$ unknown degrees of freedom
Clearly I can re-parameterize the Chi-square into a Gamma distribution and carry on. Still, I am curious if these examples violate this condition.