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?

  • $\begingroup$ The classic use of the z-score is when one assumes that underlying data is normally distributed. One needs mean and std dev to describe a distribution. The same would go for you non-normal data, you need to first find out which distribution is it and then describe it with its parameters. Once your distribution is described, only then you can say something about a data point, for example: how likely this point is generated by your distribution. $\endgroup$ – Vladislavs Dovgalecs Apr 6 '15 at 20:38
  • $\begingroup$ Z scores are not a great choice for identifying outliers even for Normal data, see this thread for a better choice: stats.stackexchange.com/questions/121071/… $\endgroup$ – Tim Apr 6 '15 at 20:53