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Thread: Events following Poisson Distribution including a fixed dead time

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    Events following Poisson Distribution including a fixed dead time




    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!

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    Re: Events following Poisson Distribution including a fixed dead time


    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?
    The mathematical explanation of a statistical procedure is really just pseudo-code, which we can make operational by translating it into real computer code. --B. Klemens

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