How to estimate a probability distribution for the waiting time before an event is observed I am trying to model a type of event that happens (once) at an unknown time. 
I would like to know: given a certain average event time, what is the probability that the event will happen within a certain time period?
I think this would be similar to a Poisson Distribution, but unlike in the Poisson Distribution, it can only happen once. I am not looking for the number of events but for the time until an event (that only occurs once) occurs.
This is being used to model restoration times in an electrical network, and the model will feed into a Monte Carlo simulation. The data is very heavily skewed. A histogram is shown here:

And here is a plot showing data that is shorter than 10% of the longest data point...

Raw data (in seconds):
[5, 1980, 5, 2, 5, 2, 5, 240, 66, 120, 9660, 3420, 10740, 48420, 87, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 9065, 40, 1, 1, 1, 2, 1, 4, 15029, 7332, 2]
 A: One way to examine your data might be by means of plots of the cumulative distribution (rather than histograms which will be very coarse).


*

*One problem is that the data does not follow a simple model. The plots are four different ways to represent the data and a straight line in those plots would correspond to linear relationship (top left), logarithmic relationship (top right), exponential relationship (bottom left), power law relationship (bottom right). None of these graphs show a clear straight line and the danger with this plots is that after taking logarithms there is often more or less a somewhat straight line but it can be meaningless.
It is likely that the data will have different regions with different behavior but it is very difficult to observe this from gazing at the data (it is too easy to find an accidental pattern that is meaningless in general), What you mostly need will be some more information/knowledge/hypotheses about how your data is expected to behave that can help/guide to form a useful and correct model (e.g. you have events that take 1 second and events that take over 10 hours, why is that? Are htey supposed to be modeled the same? Start by explaining this before your try fitting data).


*Another problem is that your data might be left censored. You have a lot of measurements at 1 and 2 seconds. The image in the top right shows a line  $(1-F(t) = a + b \log(t)$ ) that has been fitted when we exclude those 1 and 2 seconds data. It would extrapolate to observations below 1 and 2 seconds, but possibly you are unable to make those.
