aggregate 0.16.1

Tools for creating and working with aggregate probability distributions.

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aggregate: a powerful aggregate distribution modeling library in Python

Purpose

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.

Documentation

https://aggregate.readthedocs.io/

Where to get it

https://github.com/mynl/aggregate

Installation

pip install aggregate

Version History

0.16.1

• IDs can now include dashes: Line-A is a legitimate date

• Include templates and test-cases.agg file in the distribution

• Fixed mixed severity / limit profile interaction. Mixtures now work with exposure defined by losses and premium (as opposed to just claim count), correctly account for excess layers (which requires re-weighting the mixture components). Involves fixing the ground up severity and using it to adjust weights first. Then, by layer, figure the severity and convert exposure to claim count if necessary. Cases where there is no loss in the layer (high layer from low mean / low vol componet) replace by zero. Use logging level 20 for more details.

• Added more function to Portfolio, Aggregate and Underwriter classes. Given a regex it returns all methods and attributes matching. It tries to call a method with no arguments and reports the answer. more is defined in utilities and can be applied to any object.

• Moved work of qt from utilities into Aggregate` (where it belongs). Retained qt for backwards compatibility.

• Parser: power <- atom ** factor to power <- factor ** factor to allow (1/2)**(3/4)

• random` module renamed `random_agg to avoid conflict with Python random

• Implemented exact moments for exponential (special case of gamma) because MED is a common distribution and computing analytic moments is very time consuming for large mixtures.

• Added ZM and ZT examples to test_cases.agg; adjusted Portfolio examples to be on one line so they run through interpreter_file tests.

0.16.0

• Implemented ZM and ZT distributions using decorators!

• Added panjer_ab to Frequency, reports a and b values, p_k = (a + b / k) p_{k-1}. These values can be tested by computing implied a and b values from r_k = k p_k / p_{k-1} = ak + b; diff r_k = a and b is an easy computation.

• Added freq_dist(log2) option to Freq to return the frequency distribution stand-alone

• Added negbin frequency where freq_a equals the variance multiplier

0.15.0

• Added pygments lexer for decl (called agg, agregate, dec, or decl)

• Added to the documentation

• using pygments style in pprint_ex html mode

• removed old setup scripts and files and stack.md

0.14.1

• Added scripts.py for entry points

• Updated .readthedocs.yaml to build from toml not requirements.txt

• Fixes to documentation

• Portfolio.tvar_threshold updated to use scipy.optimize.bisect

• Added kaplan_meier to utilities to compute product limit estimator survival function from censored data. This applies to a loss listing with open (censored) and closed claims.

• doc to docs []

• Enhanced make_var_tvar for cases where all probabilities are equal, using linspace rather than cumsum.

0.13.0 (June 4, 2023)

• Updated Portfolio.price to implement allocation='linear' and allow a dictionary of distortions

• ordered='strict' default for Portfolio.calibrate_distortions

• Pentagon can return a namedtuple and solve does not return a dataframe (it has no return value)

• Added random.py module to hold random state. Incorporated into

  • Utilities: Iman Conover (ic_noise permuation) and rearrangement algorithms

  • Portfolio sample

  • Aggregate sample

  • Spectral bagged_distortion

• Portfolio added n_units property

• Portfolio simplified __repr__

• Added block_iman_conover to utilitiles. Note tester code in the documentation. Very Nice! 😁😁😁

• New VaR, quantile and TVaR functions: 1000x speedup and more accurate. Builder function in utilities.

• pyproject.toml project specification, updated build process, now creates whl file rather than egg file.

0.12.0 (May 2023)

• add_exa_sample becomes method of Portfolio

• Added create_from_sample method to Portfolio

• Added bodoff method to compute layer capital allocation to Portfolio

• Improved validation error reporting

• extensions.samples module deleted

• Added spectral.approx_ccoc to create a ct approx to the CCoC distortion

• qdp moved to utilities (describe plus some quantiles)

• Added Pentagon class in extensions

Earlier versions

See github commit notes.

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.

Getting started

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-13

print(f'\nProbability sum < 12 = {a.cdf(12):.3f}\nMedian = {a.q(0.5):.0f}')

>>>  Probability sum < 12 = 0.741
>>>  Median = 10

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=1727.125

See the documentation for more examples.

Dependencies

See requirements.txt.

Install from source

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.

License

BSD 3 licence.

Help and contributions

Limited help available. Email me at [e-mail].

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/.