Case | Z(λ,ν) | pmf | Distribution |
---|---|---|---|
ν=1 | e λ | \(P(X=x) = \frac {e^{-\lambda }\lambda ^{x}}{x!}, \ x=0,1,2,\ldots \) | Poisson(λ) |
ν=0,λ<1 | \(\frac {1}{1-\lambda }\) | P(X=x)=(1−λ)λ x, x=0,1,2,… | Geom(1−λ) |
ν→∞ | 1+λ | \(P(X=0) = \frac {1}{1+\lambda }; \ P(X=1) = \frac {\lambda }{1+\lambda }\) | Bernoulli\(\left (\frac {\lambda }{1+\lambda }\right)\) |