This is not a statistical question, narrowly defined, but it is a terminological question concerning a set of topics that have attracted a great deal of statistical attention, and on which I am currently trying to write a statistical software package.
If you order people from lowest income to highest, then there is a function from income level to population quantile.
There is an inverse function from the quantile to the income level.
The same ordering also defines the cumulative income less than or equal to a given level of income, or, via the income to quantile function, less than or equal to an income quantile.
Finally, if the cumulative income is divided by the total population income, the result is another kind of quantile function, of income rather than of population, that can be connected to the population quantile via the income level.
My question is whether any of these functions and inverse functions, besides the original income quantile function, has an established name or nomenclature from statistics, demographics, economics, actuarial science, or the like.
Again, my motive in asking the question is to find a literature on the way these quantities are measured, including the statistical issues involved. But I think I need the terminology first.
