# Do the location and scale parameters always control the mean/median/mode and variance, respectively?

1. Does a location parameter always control the mean/median/mode values of a PDF?
2. Does a scale parameter always control the variance of a PDF?

If the answer to any of the above questions is yes, then what about (say) Lévy distribution where the mean and the variance are infinite, while the median and mode are functions of scale parameter? Am I mixing something here?

• I think your last point is a good one - if the mean does not exist, then it is hard to think of a parameter describing the mean. – Christoph Hanck May 2 '18 at 8:46