This rather simple package providing a Julia-native implementation of the Williamson d-transform and of its inverse. See the documentations for the definitions.
Do not hesitate to open an issue and talk if you are interested.
See the following references and the documentation of the package for the definition and motivations of this (rather niche) transformation:
@book{williamson1955multiply,
title={On multiply monotone functions and their laplace transforms},
author={Williamson, Richard Edmund},
year={1955},
publisher={Mathematics Division, Office of Scientific Research, US Air Force}
}
@article{mcneil2009multivariate,
title={Multivariate Archimedean copulas, d-monotone functions and ℓ 1-norm symmetric distributions},
author={McNeil, Alexander J and Ne{\v{s}}lehov{\'a}, Johanna},
year={2009}
}
@article{mcneil2010archimedean,
title={From archimedean to liouville copulas},
author={McNeil, Alexander J and Ne{\v{s}}lehov{\'a}, Johanna},
journal={Journal of Multivariate Analysis},
volume={101},
number={8},
pages={1772--1790},
year={2010},
publisher={Elsevier}
}
@book{durante2015principles,
title={Principles of copula theory},
author={Durante, Fabrizio and Sempi, Carlo},
year={2015},
publisher={CRC press}
}If you end up using these routines in a scholarly work, please cite this work using the following bibtex:
@article{Laverny2024,
author = {Oskar Laverny and Santiago Jimenez},
title = {Copulas.jl: A fully Distributions.jl-compliant copula package},
journal = {Journal of Open Source Software},
doi = {10.21105/joss.06189},
url = {https://doi.org/10.21105/joss.06189},
year = {2024},
publisher = {The Open Journal},
volume = {9},
number = {94},
pages = {6189}
}