Parameters (statistics)
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.
definition
Be a sample. A function is called a measure of position if it is translation-equivalent:
- With
Examples
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:
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 :
- empirical variance , also called (ambiguous) sample variance, the mean squared deviation from the arithmetic mean
- Empirical standard deviation , the square root of the empirical variance
- Span , (the difference between the largest and smallest observation English range )
- Mean absolute deviation from the arithmetic mean
- Interquartile range , which contains the middle 50% of the observations (English interquartile range )
Concentration parameters
- Absolute concentration
- Relative concentration
- Atkinson measure
- Gini coefficient from the Lorenz curve
- Herfindahl index
- Hoover inequality
- Rosenbluth index
- Theil index
Shape dimensions or parameters
Individual evidence
- ^ Norbert Henze: Measure and probability theory (Stochastics II) . Karlsruhe 2010, p. 127 .
- ^ Andreas Büchter, H.-W. Henn: Elementary Stochastics - An Introduction . 2nd Edition. Springer, 2007, ISBN 978-3-540-45382-6 , pp. 71 .