The theorem relating structure of the likelihood to the concept of the sufficient statistic. Officially the necessary and sufficient condition which a statistic S be sufficient for the parameter θ is that the likelihood, l(θ; y) can be expressed in the form given below;

 

For instance, if Y1; Y2; ... ; Yn are the independent random variables from the Poisson distribution with the mean of μ, the likelihood is given by the following formula;

 
which can be factorized into the following equation