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Results tagged with poisson-distribution
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user 151977
A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.
1
vote
1
answer
154
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Data of daily counts modelled as Poisson process: should it be compound?
I understand that one of the basic assumptions of a Poisson process is that in a small enough interval, the probability of more than one arrival is negligible.
In my case, I have data that shows the …
- 697
8
votes
3
answers
6k
views
MLE for a homogeneous Poisson process?
If we have a data set consisting of event times $\{t_1, t_2, \ldots, t_N\}$ and would like to model this as a Poisson process with intensity $\lambda$, how do we do it? Intuitively, I would expect tha …
- 697
5
votes
1
answer
3k
views
Proof that the $r$'th factorial moment of a $Po(\lambda)$ random variable is $\lambda^r$?
If $X \sim Po(\lambda)$ then $E\left[X(X-1)\cdots(X-r+1)\right] = \lambda^r$.
Is there a straightforward way to see this without the use of moment generating functions?
I can get as far is $$E\left[ …
- 697