# Parametric model

In statistics, a **parametric model** is a parametrized family of probability distributions, one of which is presumed to describe the way a population is distributed.

## Examples

- For each real number μ and each positive number σ
^{2}there is a normal distribution whose expected value is μ and whose variance is σ^{2}. Its probability density function is

Thus the family of normal distributions is parametrized by the pair (μ, σ^{2}).

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

- For each positive real number λ there is a Poisson distribution whose expected value is λ. Its probability mass function is

Thus the family of Poisson distributions is parametrized by the positive number λ.

The family of Poisson distributions is an exponential family.