Dispersion index

The dispersion index (short: DI , dispersion from Latin dispersio = "dispersion" or dispergere = "distribute, spread, disperse") or variation factor ( V _f ) is a key figure in mathematical statistics for assessing the distribution pattern of the scattering of a probability distribution . The agreement or real deviation of the value distribution with a Poisson distribution is considered. The distribution patterns can be:

random,
evenly or
grouped.

Let the variance and the arithmetic mean of the elements of a sample be , then the following applies for the dispersion index : ${\ displaystyle s ^ {2}}$ ${\ displaystyle {\ bar {x}}}$ ${\ displaystyle DI}$

{\ displaystyle DI = {\ frac {s ^ {2}} {\ bar {x}}}}

.

After that, however, this assumption must be verified, e.g. B. by means of the chi-square goodness-of-fit test .

Application examples

In ecology , for example, the random, even or grouped distribution related to plants ( vegetation ecology ), animals or other carriers of characteristics can be considered.

The distribution rate of DNA sequence differences between different groups of animals can differ significantly from ratings without this index.

Individual evidence

↑ Hans-Werner Griepentrog: For the evaluation of longitudinal distributions in seed drills. In: Landtechnik . Volume 46, Volume 11, No. 91, p. 550 (PDF).
↑ Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 244
↑ Ziheng Yang, Rasmus Nielsen: Synonymous and nonsynonymous rate variation in nuclear genes of mammals. In: Journal of Molecular Evolution. Volume 46, No. 4, April 1998, pp. 409-418, doi : 10.1007 / PL00006320 .

[1] Hans-Werner Griepentrog: For the evaluation of longitudinal distributions in seed drills. In: Landtechnik . Volume 46, Volume 11, No. 91, p. 550 (PDF).

[2] Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 244

[3] Ziheng Yang, Rasmus Nielsen: Synonymous and nonsynonymous rate variation in nuclear genes of mammals. In: Journal of Molecular Evolution. Volume 46, No. 4, April 1998, pp. 409-418, doi : 10.1007 / PL00006320 .