Skip to main content

Tools for creating and working with aggregate probability distributions.

Project description

Latest Version Documentation Status Latest version
Supported Python versions Downloads
License Binary packages Zenodo DOI

aggregate: a powerful actuarial modeling library


aggregate builds approximations to compound (aggregate) probability distributions quickly and accurately. It can be used to solve 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.

White Paper (new July 2023)

The White Paper describes the purpose, implementation, and use of the class aggregate.Aggregate that handles the creation and manipulation of compound frequency-severity distributions.


Where to get it


To install into a new Python>=3.10 virtual environment:

python -m venv path/to/your/venv``
cd path/to/your/venv

followed by:


on Windows, or:

source /path/to/env/bin/activate

on Linux/Unix or MacOS. Finally, install the package:

pip install aggregate[dev]

All the code examples have been tested in such a virtual environment and the documentation will build.

Version History


  • Created version 0.22.0, convolation


  • Updated requirement using pipreqs recommendations

  • Color graphics in documentation

  • Added expected_shift_reduce = 16 # Set this to the number of expected shift/reduce conflicts to to avoid warnings. The conflicts are resolved in the correct way for the grammar to work.

  • Issues: there is a difference between dfreq[1] and 1 claim ... fixed, e.g., when using spliced severities. These should not occur.


  • Risk progression, defaults to linear allocation.

  • Added g_insurance_statistics to extensions to plot insurance statistics from a distortion g.

  • Added g_risk_appetite to extensions to plot risk appetite from a distortion g (value, loss ratio, return on capital, VaR and TVaR weights).

  • Corrected Wang distortion derivative.

  • Vectorized Distortion.g_prime calculation for proportional hazard

  • Added tvar_weights function to spectral to compute the TVaR weights of a distortion. (Work in progress)

  • Updated dependencies in pyproject.toml file.


  • Misc documentation updates.

  • Experimental magic functions, allowing, eg. %agg [spec] to create an aggregate object (one-liner).

  • 0.21.1 yanked from pypi due to error in pyproject.toml.


  • Moved sly into the project for better control. sly is a Python implementation of lex and yacc parsing tools. It is written by Dave Beazley. Per the sly repo on github:

    The SLY project is no longer making package-installable releases. It’s fully functional, but if choose to use it, you should vendor the code into your application. SLY has zero-dependencies. Although I am semi-retiring the project, I will respond to bug reports and still may decide to make future changes to it depending on my mood. I’d like to thank everyone who has contributed to it over the years. –Dave

  • Experimenting with a line/cell DecL magic interpreter in Jupyter Lab to obviate the need for build.


  • risk progression logic adjusted to exclude values with zero probability; graphs updated to use step drawstyle.


  • Bug fix in parser interpretation of arrays with step size

  • Added figures for AAS paper to extensions.ft and extensions.figures

  • Validation “not unreasonable” flag set to 0

  • Added aggregate_white_paper.pdf

  • Colors in risk_progression


  • sev_attachment: changed default to None; in that case gross losses equal ground-up losses, with no adjustment. But if layer is 10 xs 0 then losses become conditional on X > 0. That results in a different behaviour, e.g., when using dsev[0:3]. Ripple through effect in Aggregate (change default), Severity (change default, and change moment calculation; need to track the “attachment” of zero and the fact that it came from None, to track Pr attaching)

  • dsev: check if any elements are < 0 and set to zero before computing moments in dhistogram

  • same for dfreq; implemented in validate_discrete_distribution in distributions module

  • Default recommend_p=0.99999 set in constsants module.

  • interpreter_test_suite renamed to run_test_suite and includes test to count and report if there are errors.

  • Reason codes for failing validation; Aggregate.qt becomes Aggregte.explain_validation


  • Fixed reinsurance description formatting

  • Improved splice parsing to allow explicit entry of lb and ub; needed to model mixtures of mixtures (Albrecher et al. 2017)

0.18.0 (major update)

  • Added ability to specify occ reinsurance after a built in agg; this allows you to alter a gross aggregate more easily.

  • Underwriter.safe_lookup uses deepcopy rather than copy to avoid problems array elements.

  • Clean up and improved Parser and grammar

    • atom -> term is much cleaner (removed power, factor; now managed with prcedence and assoicativity)

    • EXP and EXPONENT are right associative, division is not associative so 1/2/3 gives an error.

    • Still SR conflict from dfreq [ ] [ ] because it could be the probabilities clause or the start of a vectorized limit clause

    • Remaining SR conflicts are from NUMBER, which is used in many places. This is a problem with the grammar, not the parser.

    • Added more tests to the parser test suite

    • Severity weights clause must come after locations (more natural)

    • Added ability for unconditional dsev.

    • Support for splicing (see below)

  • Cleanup of Aggregate class, concurrent with creating a cheat sheet

    • many documentation updates

    • plot_old deleted

    • deleted delbaen_haezendonck_density; not used; not doing anything that isn’t easy by hand. Includes dh_sev_density and dh_agg_density.

    • deleted fit as alternative name for approximate

    • deleted unused fields

  • Cleanup of Portfolio class, concurrent with creating a cheat sheet

    • deleted fit as alternative name for approximate

    • deleted q_old_0_12_0 (old quantile), q_temp, tvar_old_0_12_0

    • deleted plot_old, last_a, _(inverse)_tail_var(_2)

    • deleted def get_stat(self, line='total', stat='EmpMean'): return self.audit_df.loc[line, stat]

    • deleted resample, was an alias for sample

  • Management of knowledge in Underwriter changed to support loading a database after creation. Databases not loaded until needed - alas that includes printing the object. TODO: Consider a change?

  • Frequency mfg renamed to freq_pgf to match other Frequency class methods and to accuractely describe the function as a probability generating function rather than a moment generating function.

  • Added introspect function to Utilities. Used to create a cheat sheet for Aggregate.

  • Added cheat sheets, completed for Aggregate

  • Severity can now be conditional on being in a layer (see splice); managed adjustments to underlying frozen rv using decorators. No overhead if not used.

  • Added “splice” option for Severity (see Albrecher et. al ch XX) and Aggregate, new arguments sev_lb and sev_ub, each lists.

  • defaults update argument to None, which uses the object default.

  • pretty printing: now returns a value, no tacit mode; added _html version to run through pygments, that looks good in Jupyter Lab.


  • Adjusted pyproject.toml

  • pygments lexer tweaks

  • Simplified grammar: % and inf now handled as part of resolving NUMBER; still 16 = 5 * 3 + 1 SR conflicts

  • Reading databases on demand in Underwriter, resulting in faster object creation

  • Creating and testing exsitance of subdirectories in Undewriter on demand using properties

  • Creating directories moved into Extensions

  • lexer and parser as properties for Underwriter object creation

  • Default recommend_p changed from 0.999 to 0.99999.

  • recommend_bucket now uses p=max(p, 1-1e-8) if severity is unlimited.

0.17.0 (July 2023)

  • more added as a proper method

  • Fixed debugfile in which stops installation if not None (need to enure the directory exists)

  • Fixed build and MANIFEST to remove build warning

  • parser: semicolon no longer mapped to newline; it is now used to provide hints notes

  • recommend_bucket uses p=max(p, 1-1e-8) if limit=inf. Default increased from 0.999 to 0.99999 based on examples; works well for limited severity but not well for unlimited severity.

  • Implemented calculation hints in note strings. Format is k=v; pairs; k bs, log2, padding, recommend_p, normalize are recognized. If present they are used if no arguments are passed explicitly to build.

  • Added interpreter_test_suite() to Underwriter to run the test suite

  • Added test_suite_file to Underwriter to return Path to test_suite.agg` file

  • Layers, attachments, and the reinsurance tower can now be ranges, [s:f:j] syntax

0.16.1 (July 2023)

  • 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 (June 2023)

  • 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 (June 2023)

  • 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

0.14.1 (June 2023)

  • Added 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 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

  • Added example use of the Pollaczeck-Khinchine formula, reproducing examples from the actuar` risk vignette to Ch 5 of the documentation.

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.

Issues and Todo

  • Treatment of zero lb is not consistent with attachment equals zero.

  • Flag attempts to use fixed frequency with non-integer expected value.

  • Flag attempts to use mixing with inconsistent frequency distribution.

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]')
>>>        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')
>>>       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.


See requirements.txt.

Install from source

git clone --no-single-branch --depth 50 .

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 script.


BSD 3 licence.

Help and contributions

Limited help available. Email me at

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:

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

aggregate-0.22.0.tar.gz (349.0 kB view hashes)

Uploaded Source

Built Distribution

aggregate-0.22.0-py3-none-any.whl (355.7 kB view hashes)

Uploaded Python 3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page