Skellam distribution

The Skellam distribution is the discrete probability distribution of the difference N 1 − N 2 {displaystyle N_{1}-N_{2}} of two statistically independent random variables N 1 {displaystyle N_{1}} and N 2 , {displaystyle N_{2},} each Poisson-distributed with respective expected values μ 1 {displaystyle mu _{1}} and μ 2 {displaystyle mu _{2}} . It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in sports where all scored points are equal, such as baseball, hockey and soccer. The Skellam distribution is the discrete probability distribution of the difference N 1 − N 2 {displaystyle N_{1}-N_{2}} of two statistically independent random variables N 1 {displaystyle N_{1}} and N 2 , {displaystyle N_{2},} each Poisson-distributed with respective expected values μ 1 {displaystyle mu _{1}} and μ 2 {displaystyle mu _{2}} . It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in sports where all scored points are equal, such as baseball, hockey and soccer.