# Location parameter

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In statistics, a **location family** is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter , 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

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Here, is called the **location parameter**. Examples of location parameters include the mean, the median, and the mode.

Thus in the one-dimensional case if is increased, the probability density or mass function shifts rigidly to the right, maintaining its exact shape.

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 is the location parameter, *θ* represents additional parameters, and is a function parametrized on the additional parameters.

## Additive noiseEdit

An alternative way of thinking of location families is through the concept of additive noise. If is a constant and *W* is random noise with probability density then has probability density and its distribution is therefore part of a location family.