Scale parameter
From Encyclopedia of Mathematics
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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Scale_parameter&oldid=48615
Scale parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Scale_parameter&oldid=48615
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article