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Let [itex] n_1 [/itex] ~ Poisson ([itex] \lambda_1 [/itex]) and [itex] n_2 [/itex] ~ Poisson ([itex]\lambda_2[/itex]).

Now define [itex] n=n_1-n_2 [/itex]. We know [itex] n [/itex] has "Skellam distribution" with mean [itex]\lambda_1-\lambda_2[/itex] and variance [itex] \lambda_1+\lambda_2[/itex], which is not easy to deal with.

I want to find the [itex] Pr(n \geq 0) [/itex]. Is it possible to find a good approximation for the above probability by employing an approximated "Gaussian distribution"? If "Gaussian" is not a good candidate, which distribution can I replace it with?

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# Approximation of skellam distribution by a Gaussian one

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