This is a somewhat general question. For the normal distribution we have the handy concept of the z-score that can be used to measure distance from the mean in a standardized way. I've encountered a situation where I'm working with more of a gamma distribution that is somewhat right-skewed. The objective is to measure individual performers relative to some central tendency (e.g. this person is 1.5 standard deviations above the mean), but I am not aware of a z-score analogue for a gamma distribution.
Firstly, is this an appropriate way to conceptualize the problem? If so, is there a z-score analogue for the gamma? Thanks in advance.