extremeloss

Extreme value analysis for insurance losses: POT/GPD, GEV, and tail risk with uncertainty.

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Overview

extremeloss estimates the part of the distribution the data barely shows you: peaks-over-threshold fitting of the generalized Pareto distribution, block-maxima fitting of the GEV with uncertainty quantification, threshold selection diagnostics, tail-index estimators, return periods and levels, and body–tail splicing that plugs a fitted tail onto any lossmodels severity.

Fits report parameter uncertainty rather than point estimates alone, and the tail measures (VaR, TVaR, tail probabilities, return levels) quote unconditional, ground-up results.

Installation

pip install extremeloss

Diagnostic plots require the plotting extra:

pip install "extremeloss[plot]"

Requires Python 3.10 or newer.

Quick start

import numpy as np
from extremeloss import fit_pot

losses = np.random.default_rng(0).pareto(2.5, 50_000) * 1000  # heavy-tailed sample

fit = fit_pot(losses, threshold=np.quantile(losses, 0.95))    # -> GPD fit
print("shape xi      :", fit.xi)
print("scale beta    :", fit.beta)
print("99.5% VaR     :", fit.var(0.995))
print("99.5% TVaR    :", fit.tvar(0.995))
print("P(loss > 50k) :", fit.tail_probability(50_000))
print(fit.summary())

What's inside

  • Peaks over threshold — GPD fitting with parameter uncertainty and functional forms when parameters are already known.
  • Block maxima — GEV fitting, diagnostics, and uncertainty quantification.
  • Threshold selection — mean-excess and stability diagnostics.
  • Tail indices — Hill-type and related estimators.
  • Tail measures — VaR, TVaR, tail probabilities, return periods and levels, importance sampling for rare events.
  • Integration — body–tail splicing onto lossmodels severities; optional plotting via the plot extra.

The full API reference and end-to-end worked examples live at openactuarial.org/extremeloss.html.

The OpenActuarial ecosystem

extremeloss is one of seven packages that share conventions — tidy tables, explicit distribution parameterizations, reproducible random-number handling — and compose across package seams:

Package Role
actuarialpy Calculation primitives the workflow packages build on
experiencestudies Experience reporting, actual-vs-expected, claimant and concentration analysis
projectionmodels Claim, premium, and expense projection over a renewal horizon
ratingmodels Manual and experience rating, credibility, indication, GLM relativities
lossmodels Severity and frequency fitting, aggregate loss distributions
extremeloss Extreme-value tails: POT/GPD, GEV, return levels, splicing
risksim Portfolio Monte Carlo, dependence, reinsurance contracts, risk measures

Install everything at once with pip install openactuarial.

Development

git clone https://github.com/OpenActuarial/extremeloss
cd extremeloss
python -m pip install -e ".[dev]"
pytest
ruff check src tests

CI runs the same gate on Python 3.10–3.14 across Linux and Windows.

Versioning and stability

All ecosystem packages are pre-1.0: minor releases may change APIs, and every release is documented in CHANGELOG.md. Current per-package API stability is tracked at openactuarial.org/stability.html.

License

MIT — see LICENSE.

Project links

Data verified by PyPI on Jul 13, 2026
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Credits

Author: Michael Bryant

GitHub Statistics

Data verified by PyPI on Jul 13, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

MIT
View SPDX License List

Requires

Python >=3.10

Provides Extra

actuarialpy dev plot splice

Tags

actuarial extreme value theory rare events risk simulation tail risk

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