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Results tagged with poisson-process
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user 10479
For questions about the theory or applications of the Poisson process, one of the most widely applied point processes in statistics and elsewhere.
3
votes
Accepted
Confusion about Poisson rectangular pulse model
The integral expression for $Y(t)$ refers to some stochastic calculus
involving the Poisson process. However it can be understood as a sum
of random infinitesimal contributions and handled as such on …
- 5,716
1
vote
Accepted
Is it valid to simulate a shot noise Poisson process with discretization (R)
Let us derive the simulation. It will be enough to consider one of the two
process $x^{+}_t$ and $x^{-}_t$, that we can denote by $x(t)$. It has the representation $$ x(t) = \sum_{\{k: \, T_k \leq t\} …
- 5,716
1
vote
Derivation of probability under assumption of Poisson process
An interesting feature of the Poisson Process is that the Poisson
distribution can be derived from properties of the Point Process such
as orderliness and complete independence. See e.g. section 1.2 …
- 5,716
7
votes
Accepted
Poisson Process in R from exponential distribution
Basically, you need to compute the successive arrivals $S_i$ for
$i=1$, $2$, $\dots$ as cumulative sums of independent exponential
interarrivals. So the two main ingredients here are rexp and
cumsum. …
- 5,716