# Coefficient of dispersion

﻿
Coefficient of dispersion

In statistics, the coefficient of dispersion, also known as the Fano factor, is a measure used to quantify whether a set of observed occurrences are relatively clustered or dispersed compared to a standard statistical model. In this context, the observed dataset may consist of the times of occurrence of predefined events, such as earth-quakes in a given region over a given magnitude, or of the locations in geographical space of plants of a given species. Details of such occurrences are first converted into counts of the numbers of events or occurrences in each of a set of equal-sized time- or space-regions. The coefficient of dispersion is defined as the ratio of the variance σ2 to the mean μ,

: $D = \left\{sigma^2 over mu \right\},$

where the data from which the mean and variance are calculated are the counts of the numbers of occurrences across the set of intervals. The "intervals" here may be intervals in time or small regions in space. In the usual way, population and sample values of the measure can be defined.

The relevance of the coefficient of dispersion is that it has a value of one when the probability distribution of the number of occurrences in an interval is a Poisson distribution. Thus the measure can be used to assess whether observed data can be modeled using a Poisson process.

When the coefficient of dispersion is less than 1, a dataset is said to be "under-dispersed": this condition can relate to patterns of occurrence that are more regular than the randomness associated with a Poisson process. If the coefficient of dispersion is larger than 1, a dataset is said to be "over-dispersed": this can correspond to the existence of clusters of occurrences. In terms of the interval-counts, over-dispersion corresponds to there being more intervals with low counts and more intervals with high counts, compared to a Poisson distribution: in contrast, under-dispersion is characterised by there being more intervals having counts close to the mean count, compared to a Poisson distribution.

ee also

* Fano factor

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• coefficient de dispersion magnétique — magnetinės sklaidos koeficientas statusas T sritis radioelektronika atitikmenys: angl. magnetic dispersion coefficient; magnetic leakage factor vok. Koeffizient der magnetischen Streuung, m rus. коэффициент магнитного рассеяния, m pranc.… …   Radioelektronikos terminų žodynas

• Quartile coefficient of dispersion — In statistics, the quartile coefficient of dispersion is a descriptive statistic used to make comparisons within and between data sets. The statistic is easily computed using the first ( Q 1) and third ( Q 3) quartiles for each data set. Consider …   Wikipedia

• dispersion — [ dispɛrsjɔ̃ ] n. f. • XIIIe, rare av. XVIIe; lat. dispersio, de dispersus → disperser ♦ Action de disperser, de se disperser; état de ce qui est dispersé. ⇒ dissémination, division, éparpillement. La dispersion des cendres par le vent. La… …   Encyclopédie Universelle

• coefficient de fuite magnétique — magnetinės sklaidos koeficientas statusas T sritis radioelektronika atitikmenys: angl. magnetic dispersion coefficient; magnetic leakage factor vok. Koeffizient der magnetischen Streuung, m rus. коэффициент магнитного рассеяния, m pranc.… …   Radioelektronikos terminų žodynas

• Coefficient De Variation — En théorie des probabilités et statistiques, le cœfficient de variation est une mesure de la dispersion relative : il se calcule comme le rapport entre l écart type et la moyenne . Ce nombre est sans unité ; c est une des raisons pour… …   Wikipédia en Français

• Coefficient of variation — In probability theory and statistics, the coefficient of variation (CV) is a normalized measure of dispersion of a probability distribution. It is also known as unitized risk or the variation coefficient. The absolute value of the CV is sometimes …   Wikipedia

• Dispersion statistique — La dispersion représente la variabilité ou l étendue des différentes valeurs que peut prendre une variable. En statistiques, il existe différentes mesure de la dispersion. Les plus courantes sont : la variance, l écart type ou encore l écart …   Wikipédia en Français

• Dispersion (optics) — This article is about dispersion of waves in optics. For other forms of dispersion, see Dispersion (disambiguation). In a prism, material dispersion (a wavelength dependent refractive index) causes different colors to refract at different angles …   Wikipedia

• Coefficient d'aplatissement — Kurtosis En théorie des probabilités et en statistiques, le kurtosis (mot d origine grec ), plus souvent traduit par coefficient d aplatissement, ou coefficient d aplatissement de Pearson, correspond à une mesure de l aplatissement, ou a… …   Wikipédia en Français

• Coefficient Of Variation - CV — A statistical measure of the dispersion of data points in a data series around the mean. It is calculated as follows: The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for… …   Investment dictionary