# Scale parameter

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.

#### Comments

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.

#### References

[a1] | L. Breiman, "Statistics with a view towards applications" , Houghton Mifflin (1973) pp. 34–40 |

**How to Cite This Entry:**

Scale parameter. A.V. Prokhorov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Scale_parameter&oldid=13206