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Parametric family : ウィキペディア英語版 | Parametric family
In mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose definitions depend on a set of parameters. Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc. ==In probability and its applications==
For example, the probability density function of a random variable ''X'' may depend on a parameter . In that case, the function may be denoted to indicate the dependence on the parameter . 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 ''parametric family'' of densities is the set of functions , where denotes the set of all possible values that the parameter can take. In particular the normal distribution is a family of similarly shaped distributions parametrized by their mean and their variance. 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.
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