The variance of binomial distribution is π π ( ) 1− R, while the variance
of Poisson distribution is equal to the mean of the distribution
πR. Therefore, the Poisson variance will always overestimate the binomial
distribution variance by an overestimation factor which can
be defined as the ratio between the Poisson variance and binomial
variance:
a e T = − 1 1( ) π = λ .