Summary statistics | Statistical parameters

Location parameter

In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter , which determines the "location" or shift of the distribution. In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways: * either as having a probability density function or probability mass function ; or * having a cumulative distribution function ; or * being defined as resulting from the random variable transformation , where is a random variable with a certain, possibly unknown, distribution (See also ). A direct example of a location parameter is the parameter of the normal distribution. To see this, note that the probability density function of a normal distribution can have the parameter factored out and be written as: thus fulfilling the first of the definitions given above. The above definition indicates, in the one-dimensional case, that 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. (Wikipedia).

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Related pages

Scale parameter | Normal distribution | Location test | Probability density function | Probability mass function | Statistical parameter | Central tendency | Statistics | Probability distribution | Location–scale family | Cumulative distribution function | Invariant estimator