Predicting occurence of events

Question

If the sampling time interval is 10 sec and 3 events occur during the interval the first event occurs at the 4th sec , the second event occurs at the 7th sec and 8th event occurs at 8sec. Is there a way i could predict when the next event occurs ?? IS there a mathematical formula for this ? Any suggestion what i should be looking into

Answer 1

The simplest possible model that could represent your situation is a Poisson process, where each event is independent from the previous one, and the arrival rate doesn't change. In that case, estimating the arrival rate is fairly straightforward, and you can predict (or simulate) how low it will take for the next event to happen, from any given time.

Two broad situations would make that model somewhat inadequate: 1) Each event is not independent of the previous event(s). For instance, event happen in clusters, or it's less likely to observe an event right after another one happened. In that case, you may look into modeling your process as a Markov chain, where each event depends on the previous state of the system.

2) The arrival rate is not stationary. For instance, the arrival rate increases or decreases over time. In that case, you need to consider how to model that.

Hope this helps!