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Consider M events that are all independent and poisson distributed in occurence with individual frequencies $\{\lambda_{k}\}_{k=1}^{M}$. Once they occur, they occur with a certain severity, event $k$ has severity distribution $F_{k}(T)$. I would like to know the distribution of the second largest event.

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    If an event is Poisson distributed, does that mean it can occur more than once?2011-10-23
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    Yes, all events may occur more than once2011-10-23
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    I presume that by the second largest event you mean the second most severe event. Since the events all occur arbitrarily often over time, with varying severities, it doesn't make sense to speak of "the" second most severe event without saying something about the time span over which the events are compared. By the distribution of the second largest event, do you mean its severity distribution? I'd expect that you'd have to say something about $F_k(T)$ to say anything useful about that.2011-10-23
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    Yes by second largest event i mean the second most severe outcome of any event. I actually know the distribution so it is given by D(T)=e^{\lambda(1-F(T))}(1+\lambda(1-F(T)) where F(T)=P(event\: severity2011-10-23

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