Severity and frequency fitting and aggregate loss distributions.
lossmodels covers the loss-distribution workflow from data to aggregate:
a severity catalog spanning the classic distributions and the transformed
beta and transformed gamma families, frequency models, maximum likelihood
that is truncation- and censoring-aware, fit diagnostics and model selection,
and aggregate distributions via simulation, FFT, and Panjer recursion.
Every severity model shares one interface — moments, quantiles, limited expected values, increased-limits tables — so fitted models drop directly into coverage modifications, aggregates, and the wider ecosystem.
pip install lossmodelsRequires Python 3.10 or newer.
from lossmodels import Poisson, Lognormal, CollectiveRiskModel
freq = Poisson(lam=2.0)
sev = Lognormal(mu=10.0, sigma=0.8)
model = CollectiveRiskModel(freq, sev)
print("Mean :", model.mean())
print("Variance :", model.variance())
print("VaR 95% :", model.var(0.95))
print("TVaR 95% :", model.tvar(0.95))
samples = model.sample(50_000, rng=0)
print("Simulated mean:", samples.mean())- Severity — classic and extended catalogs (including the transformed beta and transformed gamma families) behind one shared interface, plus increased-limits and loss-elimination tables.
- Frequency — Poisson, negative binomial, and related counting models.
- Estimation — MLE with truncation and censoring support, parameter uncertainty, goodness-of-fit diagnostics, and model comparison.
- Aggregate —
CollectiveRiskModelsimulation, FFT and Panjer recursion, stop-loss and risk measures. - Coverage — deductibles, limits, and coinsurance applied analytically.
- Empirical — nonparametric counterparts for validation.
The full API reference and end-to-end worked examples live at openactuarial.org/lossmodels.html.
lossmodels is one of eight 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 |
| reservingmodels | Claims development and stochastic reserving: chain ladder, BF, Mack, ODP bootstrap |
| 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.
git clone https://github.com/OpenActuarial/lossmodels
cd lossmodels
python -m pip install -e ".[dev]"
pytest
ruff check src testsCI runs the same gate on Python 3.10–3.14 across Linux and Windows.
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.
MIT — see LICENSE.