- the interarrival times between events are well described by an
**exponential distribution** - the probability of ocurrence of events at any given year are described by a
**Poisson distribution** - and the duration of events is described by a
**Gamma distribution**

then the sequence has been generated by a

**Poisson stochastic process**.
And, E. Gumbel showed that the

**distribution of maximum values**taken from samples of an**exponential distribution**, converges to the**Gumbel distribution**. Therefore,*the events' maximum interarrival times generated by a Poisson process, are Gumbel distributed*.
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