I was taught in school that Poisson distribution is usually used to model rare events. And I understand the Poisson process is such that the probability of an event in one interval is independent of another interval and the probability depends on the length of the interval. However, I don't understand why an event has to be a rare one. Anyone knows? Thanks! =)
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You can make thé parameter take values small enough to fit any average frequency. – mookid Mar 13 '14 at 11:13
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L'espérance de ton processus est intensité x t. Donc en choisissant l'intensité tu peux obtenir une frequence rare. – mookid Mar 13 '14 at 12:06
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L'intensité c'est le nombre moyen de réalisations par unité de temps! – mookid Mar 13 '14 at 12:19
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Pas de souci. Je te fais une petite synthèse dans une réponse ;) – mookid Mar 13 '14 at 12:48
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pour des questions de modélisation aléatoire, cross validated est un bon endroit ;) – mookid Mar 13 '14 at 13:00
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un petit up ne ferait pas de mal :) – mookid Mar 13 '14 at 13:16
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tu dois pouvoir accepter ma réponse normalement, non ? – mookid Mar 13 '14 at 13:27
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Je ne pense pas ;) à la prochaine! – mookid Mar 13 '14 at 13:30
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For a Poisson process $X\sim P(\lambda)$:
- the increments are independant with the same distribution
- the average increment of the process in an interval of size $\Delta t$ is $E[X_{t_0+\Delta t} - X_{t_0}] = \lambda\Delta t$, so the empirical average number of realizations on the whole time of the empirical data is a good way to choose the parameter of the Poisson process
- when a certain interval is likely to be contain a big increment, the modelization via a Poisson process (or any other Levy process) is not a good idea...
mookid
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