KNOWPIA
WELCOME TO KNOWPIA

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.^{[1]}

Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc.^{[citation needed]}

For example, the probability density function *f _{X}* of a random variable X may depend on a parameter θ. In that case, the function may be denoted to indicate the dependence on the parameter θ. θ is not a formal argument of the function as it is considered to be fixed. However, each different value of the parameter gives a different probability density function. Then the

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 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.^{[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.^{[citation needed]}

**^**"All of Nonparametric Statistics".*Springer Texts in Statistics*. 2006. doi:10.1007/0-387-30623-4. ISBN 978-0-387-25145-5.**^**Mukhopadhyay, Nitis (2000).*Probability and Statistical Inference*. United States of America: Marcel Dekker, Inc. pp. 282–283, 341. ISBN 0-8247-0379-0.**^**"Parameter of a distribution".*www.statlect.com*. Retrieved 2021-08-04.