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Given:

  • a (large) group of people $G$
  • for each person in the group, attribute values $x,y$
  • for each person in the group, a percentile for $x$ over the entire group
  • for each person in the group, a percentile for $y$ over the entire group

Now, given that we can compute $z=\frac x y$, can we easily compute the percentile for a particular person's $z$ value, without precomputing the set of $z$ for every person?

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1 Answer 1

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If you mean that given one persons $x,y$ and their percentiles, can I compute the percentile of their $z$, you cannot. Let the person have $x=y=1$ and both their $x$ and $y$ percentiles are $50$. One distribution that supports this is have half the rest have $x=0.95, y=0.9$ and the other half have $x=2, y=1.1$ Our example person then has $z$ percentile of $0$. It should be easy to see how to make their $z$ percentile be $100$ as well.

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  • $\begingroup$ Would restricting the values to $x \ge 1, y \ge 1$ for everyone in the group have any effect? $\endgroup$
    – Realz Slaw
    Feb 24, 2015 at 7:08
  • $\begingroup$ No, you can just double all the numbers above and get the same result. $\endgroup$ Feb 24, 2015 at 15:19

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