I have a single parameter discrete probability distribution defined over the domain of non-negative integers with pmf in k of:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]Pr(k;L) = \frac{L^{k}}{k! * k! * I_{0}(2*\sqrt{L})}[/tex]

Where [tex]I_{0}()[/tex] is the modified Bessel function of the first kind with order 0.

I do know that [tex]E(k^{2}) = L[/tex].

Can anyone come up with a closed form for the distribution mean?

Does anyone recognize this distribution?

Thanks in advance,

J.

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# Anyone recognize this single parameter discrete probability distribution?

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