# Location parameter

﻿
Location parameter

In statistics, a location family is a class of probability distributions 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:$f_mu\left(x\right) = f\left(x - mu\right).$Here, "μ" is called the location parameter.

In other words, when you graph the function, 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 have the form:$f_\left\{mu, heta\right\}\left(x\right) = f_ heta\left(x-mu\right)$where "μ" is the location parameter, "θ" represents additional parameters, and $f_ heta$ is a function of the additional parameters.

An alternative way of thinking of location families is through the concept of additive noise. If "μ" is an unknown constant and "w" is random noise with probability density $f\left(w\right)$, then $x = mu + w$ has probability density $f_mu\left(x\right) = f\left(x-mu\right)$ and is therefore a location family.

ee also

* Invariant estimator
* statistical dispersion
* scale parameter

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Location — may refer to:* Location (geography), one of the five geographic themes and a specific position or point in physical space. (includes exact and relative.) * Absolute location * Content location in HTTP headers: a Uniform Resource Identifier *… …   Wikipedia

• Location-scale family — In probability theory, especially as that field is used in statistics, a location scale family is a family of univariate probability distributions parametrized by a location parameter mu; and a scale parameter sigma; ge; 0; if X is any random… …   Wikipedia

• Location estimation in sensor networks — Location estimation in wireless sensor networks is the problem of estimating the location of an object from a set of noisy measurements, when the measurements are acquired in a distributedmanner by a set of sensors.MotivationIn many civilian and… …   Wikipedia

• Location — [lə(ʊ)ˈkeɪʃən] ist ein aus dem englischen Sprachgebrauch eingeführter Begriff, welcher in der deutschen Übersetzung synonym für die Lage, den Standort oder die Position verwendet wird. Inhaltsverzeichnis 1 Etymologie 2 Verwendung 2.1 Lokation …   Deutsch Wikipedia

• Parameter space — In generative art people talk about parameter space as the set of possibleparameters for a generative system. In statistics one can study the distribution of a random variable. Several models exist, the most common one being the normal… …   Wikipedia

• Location Update — Das Telefon teilt mit einem Location Update dem Netz mit, in welcher Zelle innerhalb welcher LA es sich befindet. Innerhalb einer Location Area kann sich das Telefon frei bewegen. Ein Location Update findet statt a.) wenn das Telefon die LA… …   Acronyms

• Location Update — Das Telefon teilt mit einem Location Update dem Netz mit, in welcher Zelle innerhalb welcher LA es sich befindet. Innerhalb einer Location Area kann sich das Telefon frei bewegen. Ein Location Update findet statt a.) wenn das Telefon die LA… …   Acronyms von A bis Z

• Scale parameter — In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution.DefinitionIf a family of… …   Wikipedia

• Shape parameter — In probability theory and statistics, a shape parameter is a kind of numerical parameter of a parametric family of probability distributions. [Everitt B.S. (2002) Cambridge Dictionary of Statistics. 2nd Edition. CUP. ISBN 0 521 81099 x]… …   Wikipedia

• Statistical parameter — A statistical parameter is a parameter that indexes a family of probability distributions. It can be regarded as a numerical characteristic of a population or a model.[1] Among parameterized families of distributions are the normal distributions …   Wikipedia