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Citation

If you use heavytails in your research, teaching, or professional work, please cite it.

Which DOI to use

The software is archived on Zenodo, which mints two kinds of DOI. They are not interchangeable and the difference matters for reproducibility.

DOI Resolves to Cite it when
10.5281/zenodo.22045594 All versions — always the most recent release You mean "this software", and the exact version is not part of the claim
10.5281/zenodo.22176409 One release only — 0.6.3, and nothing else. Each release gets its own, minted when Zenodo archives it; earlier ones are listed under "Versions" on the concept record A result depends on the version you ran, which for numerical work it usually does

The first is the concept DOI. It is the one to use by default, and the one on the badge in the README.

Reproducibility wants the version DOI

If a reviewer should be able to reproduce a number, cite the version DOI and state the version in the text. A concept DOI resolves to whatever is newest at the time of reading, which may not be what you ran. Every release has its own version DOI, listed under "Versions" on the Zenodo record.

BibTeX

Citing all versions:

@software{ribeiro_heavytails,
  author    = {Ribeiro, Diogo},
  title     = {heavytails: A Python Library for Heavy-Tailed
               Probability Distributions},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.22045594},
  url       = {https://doi.org/10.5281/zenodo.22045594}
}

Citing release 0.6.3 exactly:

@software{ribeiro_heavytails_0_6_1,
  author    = {Ribeiro, Diogo},
  title     = {heavytails: A Python Library for Heavy-Tailed
               Probability Distributions},
  year      = {2026},
  version   = {0.6.3},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.22176409},
  url       = {https://doi.org/10.5281/zenodo.22176409}
}

Other styles

APA

Ribeiro, D. (2026). heavytails: A Python library for heavy-tailed probability distributions (Version 0.6.3) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.22176409

IEEE

D. Ribeiro, "heavytails: A Python Library for Heavy-Tailed Probability Distributions," version 0.6.3, Zenodo, 2026. doi: 10.5281/zenodo.22176409.

MLA

Ribeiro, Diogo. heavytails: A Python Library for Heavy-Tailed Probability Distributions. Version 0.6.3, Zenodo, 2026, doi:10.5281/zenodo.22176409.

Chicago

Ribeiro, Diogo. 2026. "heavytails: A Python Library for Heavy-Tailed Probability Distributions." Version 0.6.3. Zenodo. https://doi.org/10.5281/zenodo.22176409.

In-text

  • "Tail indices were estimated with the Hill estimator (Hill, 1975) as implemented in heavytails (Ribeiro, 2026)."
  • "Aggregate losses were computed by Panjer recursion (Panjer, 1981) using heavytails 0.6.3 (Ribeiro, 2026)."

Cite the method as well as the software

The library is an implementation, not the source of the methods it implements. Where a result rests on a particular estimator, cite the paper it comes from alongside the software. Every one of these is listed in CITATION.cff and .zenodo.json, so the entry can be copied rather than hunted down.

What you used Cite
hill_estimator Hill (1975), 10.1214/aos/1176343247
pickands_estimator Pickands (1975), 10.1214/aos/1176343003
moment_estimator Dekkers, Einmahl & de Haan (1989), 10.1214/aos/1176347397
smoothed_hill_estimator Resnick & Stărică (1997), 10.2307/1427870
generalized_hill_estimator Beirlant, Vynckier & Teugels (1996), Bernoulli 2(4), 293–318
bias_reduced_hill_estimator Caeiro, Gomes & Pestana (2005), REVSTAT 3(2), 113–136
harmonic_moment_estimator, t_hill_estimator Beran, Schell & Stehlík (2014), 10.1007/s10463-013-0412-2
trimmed_hill_estimator, adaptive_trimmed_hill_estimator Bhattacharya, Kallitsis & Stoev (2019), arXiv:1705.03088
gpd_mle_estimator, fit_generalized_pareto Grimshaw (1993), 10.1080/00401706.1993.10485040
Peaks-over-threshold generally Balkema & de Haan (1974), 10.1214/aop/1176996548
panjer_recursion Panjer (1981), 10.1017/S0515036100006796
Anderson–Darling p-values Marsaglia & Marsaglia (2004), 10.18637/jss.v009.i02

The adaptive trimming rule is not from the paper

adaptive_trimmed_hill_estimator uses the trimmed estimator of Bhattacharya, Kallitsis and Stoev, but the rule for choosing how much to trim is a sequential exact test on the log-spacings rather than their adaptive procedure. Cite their paper for the estimator; the selection rule is part of this software.

Acknowledgement instead of citation

Where a citation is not appropriate:

"Computational analyses were performed using heavytails, a Python library for heavy-tailed distributions (https://doi.org/10.5281/zenodo.22045594)."

How the metadata is kept honest

CITATION.cff holds the shared citation fields, and .zenodo.json overrides what Zenodo would otherwise infer from the GitHub release. The two are checked against each other, including that every reference in one appears in the other:

python scripts/validate_zenodo_metadata.py

tests/test_zenodo_metadata.py runs the same checks in CI, so the two files cannot drift apart unnoticed. The release workflow is in Releasing.

Contact

If you publish work that uses heavytails, an email is welcome — knowing what the library is used for is what decides which parts of it get attention.