Parameters (statistics)

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In statistics , aggregating parameters or measures summarize the essential properties of a frequency distribution , e.g. B. a longer series of measurement data, or a probability distribution .

Some parameters of descriptive statistics correspond to the moments of random variables .

The term parameter is also used in distribution models, in which case one speaks of distribution parameters . It is then usually one of several quantities that, together with the distribution class, determine the exact form of a distribution.

Location parameters

The definitions of location parameters aim to describe the location of the sample elements or the elements of the population in relation to the measurement scale . They combine a number of values ​​or a variable that depends on chance (e.g. time until the next decay of an atom) into a single number - the central tendency - which represents the values ​​as well as possible.


Be a sample. A function is called a measure of position if it is translation-equivalent:



In descriptive statistics, the location parameters of a distribution are:

For the three first mentioned position parameters as well as mode and median see also mean .

In the case of random variables, one speaks of the expected value .

According to the definition above, the following parameters are not position measurements:

  • Geometric mean :
  • Harmonic mean :

Dispersion parameters

A measure of dispersion or measure of dispersion (also known as dispersion parameter ) is understood to be statistical key figures , the determination of which enables statements to be made about the distribution of measured values, for example from weighing and counting, around the center point. In descriptive statistics , one describes the scatter (or dispersion; also variation ) with the following measures :

Concentration parameters

Shape dimensions or parameters

Individual evidence

  1. ^ Norbert Henze: Measure and probability theory (Stochastics II) . Karlsruhe 2010, p. 127 .
  2. ^ Andreas Büchter, H.-W. Henn: Elementary Stochastics - An Introduction . 2nd Edition. Springer, 2007, ISBN 978-3-540-45382-6 , pp. 71 .