In the taxonomy of https://www.tandfonline.com/doi/abs/10.1080/00031305.1996.10473566 (see summary on Wikipedia), this would be the R-1 definition and is identical to the "population quantile" defined on Wikipedia. We currently only support the 4-9 definitions through the use of the alpha and beta keyword arguments.

The motivation is that it is sometimes nice that quantiles are based on values in the input data. This is something we have previously discussed in the context of the median function and it recently came up in JuliaData/CategoricalArrays.jl#381 (comment).

Since the R-1 definition can't be reached through special values of alpha and beta we'd need a separate interface if we are to support the new definition. One possibility is to introduce a new keyword argument, say method or definition, which takes Enum values and errors out if set simultaneously with alpha/beta.