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Say I have data from a sample of 100 experiments. For a variable, I'm interested in showing the value x with 0.9 probability of non-exceedance, which is equivalent to P90 of the sorted sample.

I'm interested in proper names for these parameters:

x is a percentile, the 90-percentile to be specific, or more generally speaking, a quantile.

90 is the rank of x in my sample. Correct?

What would be the proper name for 0.9, or 90%? Also rank? Normalized rank? Strictly speaking it is the probability of non-exceedance, but writing that in a table header is not convenient :) A short but correct name for it would be very welcome.

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    $\begingroup$ In ordinary usage 'parameter' refers to a population, not a sample. The word 'statistic' is more commonly used for samples. $\endgroup$
    – BruceET
    Commented Jul 25, 2018 at 16:46

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I would call it the level that is used to calculate the quantiles and percentiles. (I have seen this referred to as a confidence level, but I don't like the insinuation that it would mostly be used for .)

(And yes, since you have 100 observations, the rank of the 90% percentile observation is 90. If you had 200 observations, then the 90% percentile observation would have rank 180.)

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  • $\begingroup$ I have also seen it as confidence level and I don't like for the same reason you've mentioned. Level somehow has a too strong resemblance to confidence level so not my preferred option. Calling it rank is definitely wrong then. About normalized rank? if that makes sense... $\endgroup$
    – Raf
    Commented Jul 25, 2018 at 8:44

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