# Fano factor

Fano factor

In probability theory and statistics, the Fano factor [Fano, 1947] , like the coefficient of variation, is a measure of the dispersion of a probability distribution.

Fano factor is defined as

:$F=frac\left\{sigma_W^2\right\}\left\{mu_W\right\}$

where $sigma_W^2$ is the variance and $mu_W$ is the mean of a random process in some time window $W$. The Fano factor can be viewed as a kind of noise-to-signal ratio; it is a measure of the reliability with which the random variable could be estimated from a time window that on average contains several random events.

For a Poisson process, the variance in the count equals the mean count, so $F=1$

Fano factor is similar to the variance-to-mean ratio if the time window is chosen to be infinity.

In detector systems, the Fano Factor results from the energy loss in a collision not being purely statistical. The process giving rise to each individual charge carrier is not independent as the number of ways an atom may be ionized is limited by the discrete electron shells. The net result is a higher energy resolution than predicted by purely statistical considerations.

The Fano factor is a material specific value. Theoretical values (according to Alig, Bloom and Struck, 1980) are:

Si: 0.115
Ge: 0.13
GaAs: 0.10
Diamond: 0.08

ee also

* Coefficient of variation
* Ugo Fano
* Variance-to-mean ratio (or VMR)

References

* Fano, U. (1947). Ionization yield of radiations. II. The fluctuations of the number of ions. "Phys. Rev.", 72:26-29.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Fano noise — is a limiting factor in the noise characteristics of CCDs and CMOS image sensors. It can be calculated by the Fano factor. External links * [http://adsabs.harvard.edu/abs/1988SPIE..982...70J Abstract: Janesick et al. Fano noise limited CCDs] ee… …   Wikipedia

• Ugo Fano — Infobox Scientist box width = 300px name = Ugo Fano image size = 300px caption = Ugo Fano (1912 2001). Photo taken in 1978. birth date = birth date|1912|7|28|mf=y birth place = Turin, Italy death date = death date and age|2001|2|13|1912|7|28|mf=y …   Wikipedia

• Фано, Уго — В Википедии есть статьи о других людях с такой фамилией, см. Фано. Уго Фано Ugo Fano Дата рождения: 28 июля 1912(1912 07 28) Место рождения: Турин …   Википедия

• List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… …   Wikipedia

• Index of dispersion — In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, or variance to mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability… …   Wikipedia

• List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

• Variance-to-mean ratio — In probability theory and statistics, the variance to mean ratio (VMR), like the coefficient of variation, is a measure of the dispersion of a probability distribution. It is defined as the ratio of the variance sigma^2 to the mean mu ::… …   Wikipedia

• 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… …   Wikipedia

• 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

• KABBALAH — This entry is arranged according to the following outline: introduction general notes terms used for kabbalah the historical development of the kabbalah the early beginnings of mysticism and esotericism apocalyptic esotericism and merkabah… …   Encyclopedia of Judaism