Population Stability Index

The PSI is the credit-scoring industry's standard drift metric: bin a variable using the reference (training) distribution, then compare the share of the current population in each bin.

\text{PSI} = \sum_i (a_i - e_i)\ln\frac{a_i}{e_i}

where $e_i$ and $a_i$ are the expected (reference) and actual (current) proportions in bin i.

Implement:

quantile_edges(reference, bins=10): the interior bin edges at the reference's quantiles 1/bins, 2/bins, … (bins - 1 edges)
proportions(x, edges, eps=1e-4): the share of x in each bin (use np.searchsorted(edges, x, side='right') for bin indices), with each proportion floored at eps so the log is defined
psi(reference, current, bins=10)
psi_status(value): "stable" below 0.1, "moderate" below 0.25, otherwise "shifted"