In mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters.
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Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc.
In probability and its applications
For example, the probability density function
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.
In algebra and its applications
In economics, the Cobb–Douglas production function is a family of production functions parametrized by the elasticities of output with respect to the various factors of production.
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.