aggregate solves insurance, risk management, and actuarial problems using realistic models that reflect underlying frequency and severity.
It delivers the speed and accuracy of parametric distributions to situations that usually require simulation, making it as easy to work with an aggregate (compound) probability distribution as the lognormal.
aggregate includes an expressive language called DecL to describe aggregate distributions and is implemented in Python under an open source BSD-license.
https://aggregate.readthedocs.io/
https://github.com/mynl/aggregate
pip install aggregate
To get started, import build. It provides easy access to all functionality.
Here is a model of the sum of three dice rolls. The DataFrame describe compares exact mean, CV and skewness with the aggregate computation for the frequency, severity, and aggregate components. Common statistical functions like the cdf and quantile function are built-in. The whole probability distribution is available in a.density_df.
from aggregate import build, qd
a = build('agg Dice dfreq [3] dsev [1:6]')
qd(a)
>>> E[X] Est E[X] Err E[X] CV(X) Est CV(X) Err CV(X) Skew(X) Est Skew(X)
>>> X
>>> Freq 3 0
>>> Sev 3.5 3.5 0 0.48795 0.48795 -3.3307e-16 0 2.8529e-15
>>> Agg 10.5 10.5 -3.3307e-16 0.28172 0.28172 -8.6597e-15 0 -1.5813e-13print(f'\nProbability sum < 12 = {a.cdf(12):.3f}\nMedian = {a.q(0.5):.0f}')
>>> Probability sum < 12 = 0.741
>>> Median = 10The Tweedie is a common distribution used in GLM modeling. It is a compound Poisson aggregate with gamma severity. Users may be surprised at the form of the density for small p. Here is a Tweedie with mean 10, p=1.005, dispersion (phi, sigma^2)=4
t = build('agg Tweedie tweedie 5 1.005 1')
qd(t)
>>> E[X] Est E[X] Err E[X] CV(X) Est CV(X) Err CV(X) Skew(X) Est Skew(X)
>>> X
>>> Freq 4.9848 0.44789 0.44789
>>> Sev 1.003 1.003 -8.6819e-14 0.070888 0.070888 4.9123e-07 0.14178 0.14178
>>> Agg 5 4.9992 -0.00015419 0.44902 0.44885 -0.00036361 0.45126 0.44581# check variance print(1 * 5**1.005, t.agg_var)
>>> 5.04039827609 5.04039827609
aggregate can use any scipy.stats continuous random variable as a severity, and
supports all common frequency distributions. Here is a compound-Poisson with lognormal
severity, mean 50 and cv 2.
a = build('agg Example 10 claims sev lognorm 50 cv 2 poisson')
qd(a)
>>> E[X] Est E[X] Err E[X] CV(X) Est CV(X) Err CV(X) Skew(X) Est Skew(X)
>>> X
>>> Freq 10 0.31623 0.31623
>>> Sev 50 49.888 -0.0022464 2 1.9314 -0.034314 14 9.1099
>>> Agg 500 498.27 -0.0034695 0.70711 0.68235 -0.035007 3.5355 2.2421# cdf and quantiles
print(f'Pr(X<=500)={a.cdf(500):.3f}\n0.99 quantile={a.q(0.99)}')
>>> Pr(X<=500)=0.611
>>> 0.99 quantile=1727.125See the documentation for more examples.
See requirements.txt.
git clone --no-single-branch --depth 50 https://github.com/mynl/aggregate.git . git checkout --force origin/master git clean -d -f -f python -mvirtualenv ./venv # ./venv/Scripts on Windows ./venv/bin/python -m pip install --exists-action=w --no-cache-dir -r requirements.txt # to create help files ./venv/bin/python -m pip install --upgrade --no-cache-dir pip setuptools<58.3.0 ./venv/bin/python -m pip install --upgrade --no-cache-dir pillow mock==1.0.1 alabaster>=0.7,<0.8,!=0.7.5 commonmark==0.9.1 recommonmark==0.5.0 sphinx<2 sphinx-rtd-theme<0.5 readthedocs-sphinx-ext<2.3 jinja2<3.1.0
Note: options from readthedocs.org script.
BSD 3 licence.
Version numbers follow semantic versioning, MAJOR.MINOR.PATCH:
- MAJOR version changes with incompatible API changes.
- MINOR version changes with added functionality in a backwards compatible manner.
- PATCH version changes with backwards compatible bug fixes.
Limited help available. Email me at [email protected].
All contributions, bug reports, bug fixes, documentation improvements, enhancements and ideas are welcome. Create a pull request on github and/or email me.
Social media: https://www.reddit.com/r/AggregateDistribution/.