I have some data where I want to determine whether the shape of the probability distribution has changed compared to 10 years ago.
One example is that I have for various automobiles multiple measures of price at a given point in time from different used car dealers and online sellers.
make, model, year of manufacture, price
(there are further complications such as condition etc, but I've simplified the problem somewhat).
The data has a number of outliers. Is it possible to do a robust (to clarify, by robust I mean resistant to outliers) transformation that preserves the original distribution of values, but allows a comparison of probability distributions (with different means / sds) on a similar or identical scale such as [0,1].
Also, if I had an hypothesis such that maybe the distribution of prices had a different shape in the past. Is there any sensible way to combine the data from different makes and models so as to get a more accurate estimation of the shape of the distribution function, or is this completely nonsensical.
I can of course individually compare the same make, model, yr of manufacture but I'm looking at a large number of comparisons.