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The number of arrivals in time in each of my sample is one. Each arrival time is relative to another independent time event for normalization.

If the number of arrivals is more than one, the inter-arrival time could be modeled by a homogenous Poisson process, leading to an exponential distribution.

My concern is that I only have one arrival time in each of my sample. Is it right to assume an exponential distribution for this? I mean I will just collect this single arrival time from each of my sample and then fit the gathered data to an exponential distribution; or is there a "better" distribution for modeling this kind of observation?

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"all models are wrong, but some are useful" - George E. P. Box – Alex R. Jan 31 '13 at 22:57
"Each arrival time is relative to another independent time event for normalization." I don't know what that means, and I'm exceptionally good at figuring out what was intended when people use words in a less-than-standard way. I don't really understand what you're getting at. Why would a Poisson process make more sense if each data point contained more than one arrival time? – Michael Hardy Feb 1 '13 at 1:53
Thanks, Michael. That independent time event is used as a reference for all samples taken in one location. So for samples taken at another location, another independent time event is used as a reference. This normalization procedure is done at every location. Since each time reference is deterministic (calculated by geometry), it was removed in order to model only the stochastic components. I hope this made it more clear. – user60485 Feb 1 '13 at 2:32

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