# How to find and describe regularities in a distribution of interarrival times of a recurring event?

I want to see if there are regularities in interarrival times of a recurring event in discrete time. I know that I can fit distributions to the interarrival time distribution, but are there other possibilities to detect and describe regularities for the interarrival time distribution? I would like to find out how the distribution of different lengths of the interarrival times are correlated along the time axis.

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Have you plotted interarrival time versus time itself? What does that show you? – whuber Jun 4 '12 at 19:13
@ whuber - Thank's! Yes, I know to plot the data against time. I would like to have a formula for patterns among interarrival times. Are there general methods to do this? – user11749 Jun 4 '12 at 19:35
Yes, there are a huge number of such methods, because you are basically asking "how do I find a formula for one variable which appears to depend on another,* which covers the whole gamut of regression. Therefore it behooves you to be more specific, perhaps by describing your data or by sharing the kind of plot I mentioned. – whuber Jun 4 '12 at 19:39
Re your question "how would you do it with regression?" It depends on details of the data, including what they are, how they are being measured, their statistical characteristics, and what conclusions you intend to draw from the results. (Without these details, one would have to write a multi-volume textbook to give a thorough answer your question!) – whuber Jun 4 '12 at 20:27
@ whuber: Thank's! I assume the occurrence of an event in discrete time and after one such occurence I count the time steps to the next event. These time steps counted are the interarrival time. I assume, that the reoccurrences of the event are correlated. Now, I would not only like to have a fitted distribution for the interarrival times but also a description, best would be formula, for the correlated structure of the interarrival times. Maybe You have some hints how I could proceed? Possibly with regression? Or are there other methodologies? – user11749 Jun 4 '12 at 20:52
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