- Parametric model
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 familyof 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.
* For each
real numberμ and each positive number σ2 there is a normal distributionwhose expected valueis μ and whose varianceis σ2. Its probability density function is
Thus the family of normal distributions is parametrized by the pair (μ, σ2).
This parametrized family is both an
exponential familyand a location-scale family
* For each positive real number λ there is a
Poisson distributionwhose 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
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