Q&A

# In $P(X\leq q)$, what do we call $q$?

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This is a simple question, but in $P(X\leq q)=\alpha$, what do we call $q$?

I sometimes call them quantiles, for lack of a better word, but it's not correct, I think. My 'inspiration' comes from the quantile function, which for continuous distributions we'll always have $Q(\alpha)=q$.

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A quantile is an interval of values that a random variable such that all quantiles partition the range of the random variable and contain equal amounts of probability. If it does happen that $\Pr[X \le q] = \frac{1}{n}$ then $(-\infty, q]$ could be considered the first of $n$ quantiles. But $q$ itself isn't a quantile.

I would simply call $q$ an upper bound. I don't think there's any more specific word for it.

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