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Is there a formal notation for a set of quantiles of for instance x, a numerical array? This answer suggests the notation for percentile is Pi (though what to do if you already have a variable P is unclear - I presume to use Q). But how to represent a set? Strictly speaking can it be a set if two quantiles share the same value? I'm unclear if/how the notation for an array would apply here. A steer would be much appreciated.

I do note this from Wikipedia:

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But this seems aimed at identifying the "k-th" quantile.

geotheory
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  • You may want to look at https://en.wikipedia.org/wiki/Order_statistic. You could use $X_{(\lfloor np \rfloor)}$ – typewriter Jul 02 '20 at 21:51
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    Instead of a set you could regard the quantiles as a sequence $Q_1,Q_2,\dots,Q_{n-1}$ since they can contain repeat elements. As for as notation either "$Q_i$, $0<i<n$" or "$(Q_i)_{i=1}^{n-1}$" may work. –  Jul 02 '20 at 21:54
  • Could you please expand on why you need the set of values that match a certain quantile? – typewriter Jul 02 '20 at 22:05
  • @typewriter It's for an academic paper. Consider any made-up example array e.g. x = P ⋅ log r / exp(q) (1) I'd like to declare the set of quantiles/percentiles of the distribution of x in a formal way, whatever is most appropriate. – geotheory Jul 02 '20 at 23:13
  • @M.Nestor this looks promising, thanks. – geotheory Jul 02 '20 at 23:15

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