Fano factor

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the Fano factor, like the <a href="/facts/Coefficient_of_variation/V8ddKkz4">coefficient of variation</a>, is a measure of the <a href="/facts/Statistical_dispersion/xqevRHmz">dispersion</a> of a <a href="/facts/Counting_process/4pAaYF5U">counting process</a>. It was originally used to measure the <a href="/facts/Fano_noise/WgSrmwp8">Fano noise</a> in ion detectors. It is named after <a href="/facts/Ugo_Fano/BCPV455P">Ugo Fano</a>, an Italian-American physicist.
The Fano factor after a time 
 
 
 
 t
 
 
 {\displaystyle t}
 
 is defined as

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

where 
 
 
 
 
 σ
 
 t
 
 
 
 
 {\displaystyle \sigma _{t}}
 
 is the <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a> and 
 
 
 
 
 μ
 
 t
 
 
 
 
 {\displaystyle \mu _{t}}
 
 is the mean number of events of a <a href="/facts/Counting_process/4pAaYF5U">counting process</a> after some time 
 
 
 
 t
 
 
 {\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 <a href="/facts/Random_variable/TwTBXnLT">random variable</a> can be estimated after several <a href="/facts/Random_event/aJ0l4oQb">random events</a>.
For a <a href="/facts/Poisson_point_process/8uphjAUc"> Poisson counting process</a>, the variance in the count equals the mean count, so 
 
 
 
 F
 =
 1
 
 
 {\displaystyle F=1}
 
.

Fano factor open-in-new

Fano factor