I have a data set of 100,000+ event times. For this study an event begins (at time 0) and can run for an indeterminate amount of time. The bulk of events require a couple of hours to complete but there are also events that can take tens of hours to complete. I created a histogram of the times and it resembles a positively skewed distribution.
My question is: how can I determine a distribution type to model this data? For example, the data looks log-normal, but a histogram of the log of the data is not a normal distribution (it is a negatively skewed distribution). I spent some time looking at the Gamma distribution but besides visually resembling my data I don't know if Gamma is an appropriate selection. I also had a look at the type-2 Gumbel distribution but only because it is asymmetric and semi-infinite, like my data. What are the rules for picking a distribution to model a data set?