Apologies if this is an elementary question. My rusty high school understanding of statistics has left me a bit lost to the following problem.

A long tail distribution which to incoporate into my general indicator

Essentially, I have several long-tail distributions of univariate data, as pictured, which are factors I want to incorporate into a general indicator or score to rank individuals in a sample. The idea I had in mind was to score each factor giving a greater score the further along in the probability distribution and maybe a negative score if it's below the median. From my limited knowledge, z-scores are only reliable estimators when the distribution is Gaussian since it measures variance from the mean. Is MAD (median absolute deviation) a more suitable and robust estimator for this purpose?

How does one deal with such distributions? Are there more appropriate measures to get a z-score like measure? Are there better methodologies for ranking?

Any help or suggested material would be greatly appreciated!

  • 1
    $\begingroup$ What about percentiles of the distributions? If you are in the $80$th percentile for one and $20$th percentile for another, perhaps add those together to get a score of $100$ (or an average score of $50$). $\endgroup$
    – Dave
    Commented Aug 11, 2021 at 19:13

1 Answer 1


MAD could help here but I would recommend using a log transform first to get the data looking more normal looking. Your outliers may cause issues further along the road. If you'd like to stick to simpler methods you can try Robust Scaler as explained in the scikit scaler documentation:https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html


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