Location Parameter

Location Parameter

In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter μ, which determines the "location" or shift of the distribution. Formally, this means that the probability density functions or probability mass functions in this class have the form

Here, μ is called the location parameter.

In other words, when the function is graphed, the location parameter determines where the origin will be located. If μ is positive, the origin will be shifted to the right, and if μ is negative, it will be shifted to the left.

A location parameter can also be found in families having more than one parameter, such as location-scale families. In this case, the probability density function or probability mass function will be a special case of the more general form

where μ is the location parameter, θ represents additional parameters, and is a function of the additional parameters.