A so-called positional parameter, which parametrizes a family of probability distributions of one type. A distribution in with distribution function is said to belong to the same type as a fixed distribution with distribution function if . Here is the scale parameter and is the shift parameter (or centralizing parameter). The meaning of the scale parameter is as follows: If and are the distribution functions of random variables and , respectively, then a transition from to (for ) represents a change in the unit of measurement.

The (possibly multi-dimensional) parameter in the family is also called the location parameter. The whole family of distributions is sometimes called a location-scale family of distributions.

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