In mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters.^{[1]}

For example, the probability density function f_{X} of a random variable X may depend on a parameter θ. In that case, the function may be denoted $f_{X}(\cdot \,;\theta )$ to indicate the dependence on the parameter θ. θ is not a formal argument of the function as it is considered to be fixed. However, each different value of the parameter gives a different probability density function. Then the parametric family of densities is the set of functions $\{f_{X}(\cdot \,;\theta )\mid \theta \in \Theta \))$, where Θ denotes the parameter space, the set of all possible values that the parameter θ can take. As an example, the normal distribution is a family of similarly-shaped distributions parametrized by their mean and their variance.^{[2]}^{[3]}