Can I apply the Poisson distribution on the following type of data set?
I have two types of processes, each generating events. The actual data that I posses are sets of these timestamps.
The occurrences are independent and random.
Unfortunately, events are clustered because the process generating them pauses for random periods (short AND long periods of pause). It is not the pause periods that interest me, but rather the periods during which the process is on (therefore the pause periods of time should not influence my analysis).
Since the data is not uniformly distributed over time, but rather comes in clumps, I am not sure whether I can use the Poisson distribution here.
My ultimate goal is to analyze the difference in frequency between two variants of such processes. I will compute the probability distribution for each process, for the interval of a day and see how the two differ. My fear is that the pause intervals would skew the distribution so badly that they will become meaningless to my goals.
The following are histograms for the timestamps, each bin representing one day: https://dl.dropboxusercontent.com/u/17450714/i-1.jpg
If Poisson is not good for this data, how may I analyze it by excluding the huge pause periods? Cluster analysis?