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Given a sample of inter arrival times for an entity at the same location, is there a distribution that can fit such a sample?. I was thinking about poisson, but was concerned about the independence, since the next arrival may be dependent on the previous arrival time.

Or is using a time series approach better to capture trend and seasonality?.

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  • $\begingroup$ Poisson is discrete, and is normally used for counts (0,1,2, ...). Times are usually continuous, so the Poisson would not typically be suitable. You might consider something like a shifted exponential or a gamma distribution. While the time of the next arrival is obviously dependent on the time of the previous arrival, serial dependence in inter-arrival times would occur if the current gap in arrival times was related to the previous gap in arrival times. Possible, certainly, but not as obviously true. If there is such dependence, you'll likely want to model it, maybe via time series. $\endgroup$
    – Glen_b
    May 8 '14 at 22:57
  • $\begingroup$ If you have such a sample, you can assess the suitability of say a gamma model of interarrival times with perhaps a gamma probability plot (QQ plot), or by comparing a histogram with a fitted disribution, or some measure of goodness of fit. Another possibility would be to see if the cube root was close to normal. You can check for a shifted exponential by subtracting the smallest observation from all the others and checking an exponential QQ plot. You could check for serial dependence by looking at an ACF $\endgroup$
    – Glen_b
    May 8 '14 at 23:04

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