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PreprintCC BY 4.0arXiv

A multivariate unsupervised lognormal-GPD mixture for dependent losses

  • Marco Bee
  • Flavio Santi
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Abstract

We propose a multivariate two-population mixture distribution for heavy-tailed and positively skewed non-negative data. The first mixture population is a multivariate lognormal, while the second is a distribution obtained by joining univariate zero-mean generalized Pareto densities via a Gumbel copula. The model is unsupervised, since no threshold has to be set or estimated. We derive some properties of the distribution and develop an Expectation-Conditional Maximization algorithm for maximum likelihood estimation, which is found to perform well in multivariate contexts beyond the bivariate case. The finite-sample properties of the estimators are assessed by means of simulation experiments, and an empirical application to aggregated commercial property-casualty insurance claims illustrates the impact of dependence on risk estimation. All the methods are implemented in the R package MultLognGPD, available on Github.

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Cite

BibTeXRIS
BibTeX
@misc{bee2026multivariate,
  title = {{A multivariate unsupervised lognormal-GPD mixture for dependent losses}},
  author = {Marco Bee and Flavio Santi},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02148},
  eprint = {2611.02148},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02148},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A multivariate unsupervised lognormal-GPD mixture for dependent losses
AU  - Marco Bee
AU  - Flavio Santi
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02148
UR  - https://arxiv.org/abs/2611.02148
AB  - We propose a multivariate two-population mixture distribution for heavy-tailed and positively skewed non-negative data. The first mixture population is a multivariate lognormal, while the second is a distribution obtained by joining univariate zero-mean generalized Pareto densities via a Gumbel copula. The model is unsupervised, since no threshold has to be set or estimated. We derive some properties of the distribution and develop an Expectation-Conditional Maximization algorithm for maximum likelihood estimation, which is found to perform well in multivariate contexts beyond the bivariate case. The finite-sample properties of the estimators are assessed by means of simulation experiments, and an empirical application to aggregated commercial property-casualty insurance claims illustrates the impact of dependence on risk estimation. All the methods are implemented in the R package MultLognGPD, available on Github.
ER  -