Hi,
Im trying to describe some events with the Poisson distribution and overall its a really good fit. There is however a slight error in the model since there is a dead time when every event is about to happen.
Imagine for instance taking a picture with an oldfashioned polaroid camera and the success criteria is whenever i receive the actual picture as output from the camera. The time from when i press the release to the picture is in my hand is dead- there cannot be another event in this time- the camera will simply ignore my action.
What Im trying to describe works similarly
Does anyone know how to do this? I think it has to look something like this but I am not sure.. :
π = P(0|event) + P(1|event) + P(2|event)… P(n|event) + P(D)
P(0) = Poisson(0, λ(t))
P(1) = Poisson(1, λ(t-d1))
P(2) = Poisson(2, λ(t-d2))
.
.
.
P(n) = Poisson(n, λ(t-dn))
t = time left , d = dead time
In order to sum to 1 I add P(D) which Im not sure how to quantify- this is my best bid:
P(D) = P(d1|P(1)) + P(d2|P(2)) + … P(dn|P(n))
P(dn|P(x)) = dn/t
Hope somebody is great at this and willing to help me! Thank you!
Im trying to describe some events with the Poisson distribution and overall its a really good fit. There is however a slight error in the model since there is a dead time when every event is about to happen.
Imagine for instance taking a picture with an oldfashioned polaroid camera and the success criteria is whenever i receive the actual picture as output from the camera. The time from when i press the release to the picture is in my hand is dead- there cannot be another event in this time- the camera will simply ignore my action.
What Im trying to describe works similarly
Does anyone know how to do this? I think it has to look something like this but I am not sure.. :
π = P(0|event) + P(1|event) + P(2|event)… P(n|event) + P(D)
P(0) = Poisson(0, λ(t))
P(1) = Poisson(1, λ(t-d1))
P(2) = Poisson(2, λ(t-d2))
.
.
.
P(n) = Poisson(n, λ(t-dn))
t = time left , d = dead time
In order to sum to 1 I add P(D) which Im not sure how to quantify- this is my best bid:
P(D) = P(d1|P(1)) + P(d2|P(2)) + … P(dn|P(n))
P(dn|P(x)) = dn/t
Hope somebody is great at this and willing to help me! Thank you!