Location Shape Parameter

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A Location Shape Parameter is a shape parameter that ...



  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/location_parameter Retrieved:2015-6-28.
    • In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter [math]\displaystyle{ x_0 }[/math] , 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 : [math]\displaystyle{ f_{x_0}(x) = f(x - x_0). }[/math] Here, [math]\displaystyle{ x_0 }[/math] is called the location parameter. Examples of location parameters include the mean, the median, and the mode.

      Thus in the one-dimensional case if [math]\displaystyle{ x_0 }[/math] 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 : [math]\displaystyle{ f_{x_0,\theta}(x) = f_\theta(x-x_0) }[/math] where [math]\displaystyle{ x_0 }[/math] is the location parameter, θ represents additional parameters, and [math]\displaystyle{ f_\theta }[/math] is a function parametrized on the additional parameters.