MetalogPlottingPositions

Turns raw observations into the cumulative distribution function data that a metalog is parameterized by.

A metalog is fitted to points on a cumulative distribution function rather than to observations directly, so each sorted observation is paired with a plotting position. The convention used here places the i-th of m sorted values at a probability of one half less than i, divided by m, which keeps every probability strictly inside the unit interval, as the basis functions require.

For a large sample the data is instead resampled onto a fixed probability grid. That bounds the height of the design matrix without discarding the tails, since the grid is refined approaching each endpoint, which is where a metalog's shape flexibility is most needed and where evenly spaced probabilities carry the least information.