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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 f_X of a random variable ''X'' may depend on a parameter \theta . In that case, the function may be denoted f_X( \cdot \, ; \theta) to indicate the dependence on the parameter \theta . \theta 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 \Theta denotes the set of all possible values that the parameter \theta 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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