Parametric family

[1] Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc.

[citation needed] For example, the probability density function fX of a random variable X may depend on a parameter θ.

to indicate the dependence on the parameter θ. θ is not a formal argument of the function as it is considered to be fixed.

[2][3] In decision theory, two-moment decision models can be applied when the decision-maker is faced with random variables drawn from a location-scale family of probability distributions.

[citation needed] In algebra, the quadratic equation, for example, is actually a family of equations parametrized by the coefficients of the variable and of its square and by the constant term.

A graph of several normal distributions.
A graph of the probability density functions of several normal distributions (from the same parametric family).
A three-dimensional graph of a Cobb–Douglas production function .
Graphs of several quadratic equations
Graphs of several quadratic polynomials , varying each of the three coefficients independently.