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PreprintCC BY 4.0arXiv

On the asymptotic shape of quantile surfaces

  • Florian Gach
  • Simon Hochgerner
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Abstract

This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level α generated by a controlled one-dimensional distribution. Specifically, when the distribution arises as a linear combination of log-normal random variables and the control is a vector of positive coefficients, we prove that quantile surfaces are globally concave in the left tail (α→0) and globally convex in the right tail (α→1). Moreover, these surfaces exhibit asymptotic separation of scale and shape.

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Cite

BibTeXRIS
BibTeX
@misc{gach2026asymptotic,
  title = {{On the asymptotic shape of quantile surfaces}},
  author = {Florian Gach and Simon Hochgerner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.31345},
  eprint = {2609.31345},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31345},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the asymptotic shape of quantile surfaces
AU  - Florian Gach
AU  - Simon Hochgerner
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.31345
UR  - https://arxiv.org/abs/2609.31345
AB  - This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level α generated by a controlled one-dimensional distribution. Specifically, when the distribution arises as a linear combination of log-normal random variables and the control is a vector of positive coefficients, we prove that quantile surfaces are globally concave in the left tail (α→0) and globally convex in the right tail (α→1). Moreover, these surfaces exhibit asymptotic separation of scale and shape.
ER  -