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A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion.
As it turns out, uniformly distributed measures are very rigid objects. On any "decent" metric space, the uniformly distributed measures form a one-parameter linearly dependent family: Let μ and ν be uniformly distributed Borel regular measures on a separable metric space (X, d). Then there is a constant c such that μ = cν.
Such a measure is called a probability measure or distribution. See the list of probability distributions for instances. The Dirac measure δ a (cf. Dirac delta function) is given by δ a (S) = χ S (a), where χ S is the indicator function of . The measure of a set is 1 if it contains the point and 0 otherwise.
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 ...
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
It provides a measure of central tendency in higher dimensions and it is a standard problem in facility location, i.e., locating a facility to minimize the cost of transportation. [3] The geometric median is an important estimator of location in statistics, [4] because it minimizes the sum of the L 2 distances of the samples. [5]
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