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Given a set $P_i$ of probabilities and a Cumulative Distribution Function of $X$ you can find the set $X_i$ of values of $X$ corresponding to $P_i$. The $X_i$ are the "quantiles". Is there an equivalent generic term for referring to the $P_i$ corresponding to a given set of $X_i$?

You could refer to them as the CDF but in standard use that refers to the $P_i$ corresponding to all the $X_i$ rather than some designated subset of interest.

In the absence of a pre-existing name I'll probably use some awful phrase like "Corresponding Cumulative Probabilities" (abbreviated as CCP and pronounced "soviets").

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  • $\begingroup$ Aren't these usually just called the "percents" when the quantiles are referred to as percentiles? $\endgroup$
    – whuber ♦
    Commented Nov 26, 2012 at 17:01
  • $\begingroup$ @whuber Do you have any feeling for how widely used that terminology is (percents/percentiles)? I ran the query past my office-mates before posting and nobody knew a generic term. My concern with "percents" as terminology is that it is tied to a specific set of probabilities. In my line of work we frequently use deciles - percents/deciles doesn't work so well, and decs/deciles is jut mystifying. I like probtiles/quantiles because it is an obvious derivation, there is no chance of confusion with "probtiles" being used in some other sense (unlike "percents") and it is completely generic. $\endgroup$
    – Ross Gayler
    Commented Nov 26, 2012 at 20:27
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    $\begingroup$ It's common--search the Web. Some authors have attempted to refine this a little; e.g., Freedman, Pisani, & Purves (Statistics, WW Norton & Co.) state (in the context of a group of test scores), "A percentile is a score; in example 10, the 95th percentile is a score of 700. A percentile rank, however, is a percent: if you score 700, your percentile rank is 95%." "Probtile" is so etymologically bizarre (and strangely pronounced) I doubt it will ever get any currency. $\endgroup$
    – whuber ♦
    Commented Nov 26, 2012 at 20:37
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    $\begingroup$ @whuber Thanks. Now that I know where to look I can see that "quantile rank" is also used. $\endgroup$
    – Ross Gayler
    Commented Nov 26, 2012 at 22:21

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I guessed that "probtile" sounded like a good analogue to "quantile" and did a search to see if probtile exists in the wild, and it does!

"Probtile" is used in mathematical finance to mean the probability corresponding to a quantile. However, the word doesn't seem to be widely used - mostly in the writings of Gilles Zumbach of RiskMetrics Group (This 2006 paper introduces the term "probtile".) This suggests that few people feel the need for the concept and that different terms for the same concept may have been invented in different fields.

I would interested to hear of any alternatives to probtile.

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