Year: 2026
Type: preprint
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 ($α\to0$) and globally convex in the right tail ($α\to1$). Moreover, these surfaces exhibit asymptotic separation of scale and shape.
Source: arXiv (Cornell University)
Authors: Gach, Florian, Hochgerner, Simon
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214580142