EDIT: Should I better post this question in https://stats.stackexchange.com/??
NOTE: Here, I am supposing that the reader knows the difference between population (which is where a probability distribution is 'placed') and sample (data sample, sample of data...).
Is there any sort of standard notation for referring to the $i$-th quartile of a probability distribution? I mean, normally $Q_i$ is used to denote the $i$-th quartile of a data sample. I am asking about how to denote the same concept in the population.
For instance, I've seen that, while the sample $i$-th percentile is usually referred to as $P_i$ (or $p_i$), the population counterpart is denoted as $\pi_i$. It is common to use (lower) Greek letters to denote population parameters.
So, probably the most reasonable alternative would be using the (lowercase) Greek equivalent for the Latin 'Q' in order to refer to quartiles in the population. According to Wikipedia (see https://en.wikipedia.org/wiki/Koppa_(letter)), this can be either the archaic Greek letter 'koppa' (ϟ or ϙ) or the Greek letter 'kappa' ($\kappa$).
Drawbacks of each of these alternatives:
- 'ϟ' is probably too 'exotic'.
- 'ϙ' is maybe too similar to '$q$' or '$Q$'.
- '$\kappa$' is mostly identified with '$k$' rather than '$q$'.
What do you think of this possibility? Do you know any other reasonable/widespread/standard alternative?