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Results tagged with poisson-distribution
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user 42609
A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.
1
vote
Distribution of sum of two shifted Poisson
As stated in my comment, $Z-(a+b)=(Y−a)+(X−b)$, which is the sum of two Poisson distributed random variables. If $Y-a\sim\mathrm{Po}(t)$ and $X-b\sim\mathrm{Po}(r)$ are independent (which is the case …
- 558
5
votes
Accepted
Poisson distribution of two independent random variables
Since $Y\sim \mathrm{Poisson}(\mu)$, the probability generating function of $Y$ is given by
$$G_Y(z)=e^{\mu(z-1)}$$ and that of $X_1+X_2$ (by independence) as $$G_{X_1+X_2}(z)=G_{X_1}(z)G_{X_2}(z)=e^{ …
- 558