A location parameter shifts a statistical distribution without changing its shape. If 
has distribution function 
, then 
has location parameter 
and distribution function
 |
When a probability density function 
exists, the corresponding density
is
 |
Other parameters are held fixed when varying 
.
In the usual parametrization of a normal distribution, the location parameter is its mean. In general, a location parameter need not be a mean, and it remains meaningful when the mean does not exist, as for the Cauchy distribution.
