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?