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I was often wondering how to call $\beta$ of the $\beta$-quantile of a distribution. Of course, $\beta$ is a probability or proportion. But is there an official name for it?

So instead of saying "The median equals the $\beta$-quantile with $\beta = 0.5$" we could state "The Median equals the quantile with a xyz of 0.5."

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    $\begingroup$ Maybe just "left tail probability," "area to the left" or something like that. This isn't a name for the probability, but the distribution function is the function $F$ whose value at $\beta$ is equal to the probability you're referring to, at least for continuous distributions. $\endgroup$
    – dsaxton
    Commented Dec 28, 2015 at 14:34
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    $\begingroup$ It's notionally if not literally a cumulative probability. In some contexts it is also called a plotting position, especially when there is a graph in view or in mind. $\endgroup$
    – Nick Cox
    Commented Dec 28, 2015 at 16:07

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Partially answered in comments:

Maybe just "left tail probability," "area to the left" or something like that. This isn't a name for the probability, but the distribution function is the function $F$ whose value at $β$ is equal to the probability you're referring to, at least for continuous distributions.

– dsaxton

It's notionally if not literally a cumulative probability. In some contexts it is also called a plotting position, especially when there is a graph in view or in mind. – Nick Cox

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