Discrete distributions | Poisson distribution | Infinitely divisible probability distributions

Skellam distribution

The Skellam distribution is the discrete probability distribution of the difference of two statistically independent random variables and each Poisson-distributed with respective expected values and . 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 distribution is also applicable to a special case of the difference of dependent Poisson random variables, but just the obvious case where the two variables have a common additive random contribution which is cancelled by the differencing: see Karlis & Ntzoufras (2003) for details and an application. The probability mass function for the Skellam distribution for a difference between two independent Poisson-distributed random variables with means and is given by: where Ik(z) is the modified Bessel function of the first kind. Since k is an integer we have that Ik(z)=I|k|(z). (Wikipedia).

Skellam distribution
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Support (mathematics) | Moment (mathematics) | Skewness | Bessel function | Ratio distribution | Big O notation | Asymptotic expansion | Probability-generating function | Poisson distribution | Cumulant-generating function | Variance | Photon noise | Normal distribution | Convolution | Random variable | Expected value | Moment-generating function | Kurtosis | Probability mass function | Cumulant