A parametric model is a set of related mathematical equations in which alternative scenarios are defined by changing the assumed values of a set of fixed coefficients (parameters). 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.
Formally, a parametric model is the set where is the set of all possible parameters.
Thus the family of normal distributions is parametrized by the pair (μ, σ2).
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.