L-moments UQ — Python port

A Python port of the L-UQ MATLAB toolbox one directory up: distribution-independent uncertainty quantification from scarce samples, including data with extremes, using L-moments. Same method, same 9 supported distribution families, plus an interactive Streamlit UI.

Validation. Every parameter-estimation formula and distribution-parameterization/sign convention is validated against known scipy.stats ground truth — see tests/test_lmoments.py (30 tests). In addition, this port and the MATLAB implementation have been verified equivalent: on fixed reference samples, MATLAB's lmom, Parameter_estimation, and CDF_l reproduce this package's L-moments, parameter vectors, and fitted CDF values to within 1e-8 (run tests/octave_verify.m under GNU Octave, or the MATLAB suite tests/test_uq_matlab.m — both pass, the latter under MATLAB R2026a). On the same samples the package agrees with R's lmom to machine precision wherever the closed forms coincide.

Install

cd python
python3 -m venv .venv && source .venv/bin/activate
pip install -e ".[ui,dev]"

Run the tests

pytest tests/ -v

Run the illustrative example

python demo_example.py --no-show   # saves demo_example_output.png

Run the interactive UI

streamlit run app.py

Lets you paste in a sample (or generate a synthetic scarce+extreme one), see its L-moments and the ranked distribution-family match, pick a family to fit, and view the PDF/CDF fit against the sample compared with a conventional-moment (MLE) fit of the same family, plus Jensen-Shannon divergence numbers quantifying the difference.

Install

pip install lmoments-uq          # distribution name (hyphen)

The import namespace is lmoments_uq (underscore), distinct from the unrelated lmoments / lmoments3 packages on PyPI.

API

from lmoments_uq import identify_dist, parameter_estimation, pdf_l, cdf_l, random_l, js_div

result = identify_dist(x)              # {'best', 'ranking', 'L_sample'}
params = parameter_estimation(x, result['best'], *result['L_sample'])
pdf_vals = pdf_l(xgrid, result['best'], params)

# uncertainty-aware identification (bootstrap selection frequencies)
from lmoments_uq import identify_dist_bootstrap
boot = identify_dist_bootstrap(x)      # {'best','selection_frequencies','status',...}

Differences from the MATLAB version

• identify_dist returns the full ranked distance to all 9 candidate families (result['ranking']), not just the single closest match — a strict addition, useful for the UI's ranking table.
• parameter_identify(x, k) genuinely fits the top-k candidates; the MATLAB version's K argument silently breaks for K>1 because Identify_dist.m never actually returns more than one candidate.
• The Gamma distribution's location shift is applied consistently in both pdf_l and cdf_l in both implementations (MATLAB's CDF_l.m historically omitted it; fixed as of the SoftwareX/JSS submission preparation).
• kl_div(p, q) returns inf when p has mass in a bin where q has none (the mathematically correct value); MATLAB's KLDiv.m drops such bins and can return a finite — even negative — divergence there. This cannot affect js_div, whose mixture term is positive wherever p is, and js_div was verified to machine precision against scipy.spatial.distance.jensenshannon (see the divergence tests).
• weibul is supported in parameter_estimation/pdf_l/cdf_l/random_l for completeness, but — matching the MATLAB version — is not one of the families identify_dist will pick automatically.

Known limitations (inherited from the method/toolbox)

• Weibull is not offered for automatic identification (see above).
• Gumbel is the k=0 special case of the GEV curve, and Uniform is the k=1 boundary case of the GP curve, on the L-moment ratio diagram; for samples near those special cases, identify_dist can pick either the special-case family or its generalizing family. This is a property of the diagram itself, not a bug (see tests/test_lmoments.py for how this is handled in testing).