Events following Poisson Distribution including a fixed dead time

honestlyno

New Member
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! ted00

New Member
just let your observation time be everything except the dead time, like what you wrote with the (t-d) part. the denominator can then be the total non-dead time ... would this not work?