From wikipedia:
A parametric family (parametric model) is a collection of probability distributions such that each member of this collection, $P_\theta$, is described by a finite-dimensional parameter $\theta$. The set of all allowable values for the parameter is denoted $\Theta \subseteq \mathbb{R}^k$, and the family itself is written as $\mathcal{P} = \{P_\theta: \theta \in \Theta \}$.
The parametric model captures all its information about the data within its parameters. In other words, knowledge of $\theta$ yields knowledge of the entire population.
And I have the following question:
What are the possible types (categories) of estimands (i.e. unknown population characteristics) in the case of a parametric family of distributions?
I think that there are only two types of estimands in this case:
finite-dimensional parameter $\theta \in \Theta \subseteq \mathbb{R}^k$ (or its sub-vector) which indexes the parametric family $\mathcal{P}$
real-valued function of the parameter $\theta$ (or its sub-vector) denoted $g(\theta)$
We can use methods of point estimation or interval estimation to find estimates of $\theta$ or $g(\theta)$.
Are there any other types of estimands in the case of a parametric family of distributions?