Fano factor

In statistics, the Fano factor,^[1] like the coefficient of variation, is a measure of the dispersion of a counting process. It was originally used to measure the Fano noise in ion detectors. It is named after Ugo Fano, an Italian-American physicist.

The Fano factor after a time ${\displaystyle t}$ is defined as

${\displaystyle F(t)={\frac {\sigma _{t}^{2}}{\mu _{t}}},}$

where ${\displaystyle \sigma _{t}}$ is the standard deviation and ${\displaystyle \mu _{t}}$ is the mean number of events of a counting process after some time ${\displaystyle t}$. The Fano factor can be viewed as a kind of noise-to-signal ratio; it is a measure of the reliability with which the waiting time random variable can be estimated after several random events.

For a Poisson counting process, the variance in the count equals the mean count, so ${\displaystyle F=1}$.