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I have some decile distributions of income (1th to 9th decile). Now I would like to know the income of the 99th percentile. My idea is to use the nine data points that I have, to build a (probably not linear) regression model (income ~ percentile) with which I can estimate the income of the 99th percentile.

As I am not that familiar with using deciles, I wanted to know if my approach makes sense, and (if not) what else could be done.

Thank you in advance and kind regards :)

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    $\begingroup$ You're right that you're going to need a nonlinear relationship here. My guess is that there are any number of plausible fits to the known deciles that will give extraordinarily different extrapolations to the 99% point. Perhaps you can work backwards from cases with 99% known to get a rule of thumb, but it's still extrapolation written large. You presumably know all this, but it's still an exercise that requires scepticism to the maximum possible extent. $\endgroup$
    – Nick Cox
    Commented Feb 8, 2018 at 16:46
  • $\begingroup$ A large chunk of the pertinent literature is about very different probability distributions that all work well some of the time. $\endgroup$
    – Nick Cox
    Commented Feb 8, 2018 at 16:46
  • $\begingroup$ Thank you for the comments. Do you maybe have some links to the literature you are mention or more information about the distributions used? The pareto distribution seems to be often used to model the upper tail. But I might in future also be interested in the lower deciles. Do you happen to know any distribution that fits well here? $\endgroup$
    – Bobipuegi
    Commented Feb 9, 2018 at 8:23
  • $\begingroup$ wiley.com/en-gb/… $\endgroup$
    – Nick Cox
    Commented Feb 9, 2018 at 8:29

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