I am looking for some direction to see if there is an equivalent metric to a z score that could be used to quickly identify individual values in a non-normal distribution that are not likely to occur (for example, + or - 3 standard deviations).
This is really basic with a normal distribution but the data I'm dealing with is highly skewed with a very large amount of values at 0. Specifically, my data contains the geographical distance between two events that occur. Many times, the events take place in the same location, leaving a huge volume of values of 0, with the rest of the distances decreasing rapidly in frequency.
I attempted to do a log transformation but this still does not work well with the values of 0.
Again, is there something like a z score that can be used on non normal data? If not, what is the best way to find the values that are not likely to occur?