In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters.

A statistical model is a collection of probability distributions on some sample space. We assume that the collection, 𝒫, is indexed by some set Θ. The set Θ is called the parameter set or, more commonly, the parameter space. For each θ ∈ Θ, let F_θ denote the corresponding member of the collection; so F_θ is a cumulative distribution function. Then a statistical model can be written as

The model is a parametric model if Θ ⊆ ℝ^k for some positive integer k.

When the model consists of absolutely continuous distributions, it is often specified in terms of corresponding probability density functions:

where p_λ is the probability mass function. This family is an exponential family.

This parametrized family is both an exponential family and a location-scale family.

where ${\displaystyle \beta }$ is the shape parameter, ${\displaystyle \lambda }$ is the scale parameter and ${\displaystyle \mu }$ is the location parameter.

This example illustrates the definition for a model with some discrete parameters.