lossmodels 0.1.3

A Python library for actuarial loss modeling using frequency-severity methods.

lossmodels

A Python library for actuarial loss modeling using frequency–severity methods.

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Overview

lossmodels is a Python library for frequency-severity modeling, aggregate loss analysis, actuarial coverage modifications, credibility, and model fitting. It is designed for actuarial students, analysts, insurance data scientists, and quantitative developers who want a lightweight, readable implementation of core loss modeling techniques.

Highlights

• Frequency models: Poisson, Negative Binomial, Binomial, Geometric
• Severity models: Exponential, Gamma, Lognormal, Pareto, Weibull
• Empirical distributions for frequency and severity data
• Aggregate loss modeling with:
  • Monte Carlo simulation
  • Panjer recursion
  • FFT aggregation for Poisson frequency
• Risk measures:
  • VaR
  • TVaR
  • Stop-loss
  • Limited expected value
  • PMF-based risk metrics
• Coverage modifications:
  • Ordinary deductibles
  • Policy limits
  • Layers
• Estimation tools:
  • Maximum likelihood estimation
  • Method of moments
  • AIC / BIC diagnostics
  • Best-fit selection for supported severity and frequency models
• Credibility models:
  • Bühlmann
  • Bühlmann–Straub

Installation

Install from PyPI:

pip install lossmodels

Install in development mode from source:

pip install -e .

Current package metadata:

• Version: 0.1.3
• Python: >=3.10
• Core dependencies: numpy, scipy

Package Structure

lossmodels/
├── aggregate/     # aggregate loss models, discretization, Panjer, FFT, risk metrics
├── coverage/      # deductibles, limits, and layers
├── credibility/   # Bühlmann and Bühlmann–Straub credibility
├── empirical/     # empirical frequency and severity distributions
├── estimation/    # MLE, method of moments, diagnostics, model selection
├── frequency/     # discrete claim count models
├── severity/      # continuous claim severity models
└── utils/         # helper utilities

Quick Start

Frequency-Severity Aggregate Model

from lossmodels.frequency import Poisson
from lossmodels.severity import Lognormal
from lossmodels.aggregate import 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)
print("Simulated mean:", samples.mean())

Fit Models to Data

from lossmodels.estimation import (
    fit_lognormal,
    fit_poisson,
    fit_best_severity,
    fit_best_frequency,
)

freq_model = fit_poisson(freq_data)
sev_model = fit_lognormal(sev_data)

best_severity = fit_best_severity(sev_data, criterion="aic")
best_frequency = fit_best_frequency(freq_data, criterion="bic")

print(best_severity["best_name"])
print(best_frequency["best_name"])

Coverage Modifications

from lossmodels.frequency import Poisson
from lossmodels.severity import Lognormal
from lossmodels.coverage import OrdinaryDeductible, PolicyLimit, Layer
from lossmodels.aggregate import CollectiveRiskModel

base_sev = Lognormal(mu=10.0, sigma=0.8)

with_deductible = OrdinaryDeductible(base_sev, d=10_000)
with_limit = PolicyLimit(base_sev, u=50_000)
layer = Layer(base_sev, d=10_000, u=40_000)

model = CollectiveRiskModel(Poisson(lam=2.0), layer)
print(model.mean())

Available Models

Frequency

• Poisson
• NegativeBinomial
• Binomial
• Geometric

Severity

• Exponential
• Gamma
• Lognormal
• Pareto
• Weibull

Empirical

• EmpiricalFrequency
• EmpiricalSeverity

Coverage

• OrdinaryDeductible
• PolicyLimit
• Layer

Credibility

• Buhlmann
• BuhlmannStraub

Aggregate Loss Methods

The aggregate module supports multiple ways to analyze total loss.

Simulation

samples = model.sample(100_000)

Panjer Recursion

from lossmodels.aggregate import discretize_severity, panjer_recursion

pmf = discretize_severity(sev, h=100.0, max_loss=200_000.0)
agg_pmf = panjer_recursion(freq, pmf, n_steps=5000)

FFT Aggregation

from lossmodels.aggregate import fft_aggregate_poisson

agg_pmf = fft_aggregate_poisson(freq, pmf, n_steps=5000)

PMF-Based Risk Measures

from lossmodels.aggregate import var_from_pmf, tvar_from_pmf, stop_loss_from_pmf

var95 = var_from_pmf(agg_pmf, h=100.0, q=0.95)
tvar95 = tvar_from_pmf(agg_pmf, h=100.0, q=0.95)
sl = stop_loss_from_pmf(agg_pmf, h=100.0, d=50_000.0)

Estimation and Model Selection

The estimation module includes:

• MLE fitters for supported frequency and severity distributions
• method-of-moments estimators
• log-likelihood, AIC, and BIC diagnostics
• fit_best_severity(...)
• fit_best_frequency(...)

Current automated model selection support includes:

• Severity candidates: exponential, gamma, lognormal, weibull
• Frequency candidates: poisson, negbinomial

Examples

The repository currently includes the following example scripts:

• credibility_example.py
• deductible_example.py
• fit_and_compare_models.py
• fit_and_simulate.py
• layer_example.py
• limit_example.py
• panjer_vs_fft_vs_simulation.py
• panjer_vs_simulation.py
• stop_loss_example.py

Testing

Run the test suite with:

pytest -v

Run only non-slow tests with:

pytest -v -m "not slow"

Project Scope

lossmodels currently focuses on core actuarial material around frequency-severity modeling and aggregate loss methods, with readable implementations that are useful for:

• learning actuarial loss models
• prototyping insurance analytics workflows
• validating calculations against textbook-style examples
• building small actuarial tools on top of a reusable package

License

MIT License