Location model (statistics)

In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter ${\displaystyle x_{0}}$, 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, ${\displaystyle x_{0}}$ is called the location parameter. Examples of location parameters include the mean, the median, and the mode.

Thus in the one-dimensional case if ${\displaystyle x_{0}}$ is increased, the probability density or mass function shifts rigidly to the right, maintaining its exact shape.

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