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Peer-reviewedCC BY 4.0Mathematics

Robust Quantile-Structure Inversion for Cloud Model Parameter Identification

  • Peiyang Cai1
  • Wenjuan Li2
  • Weidong Rao3
  1. 1Statistics and Data Science, Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63130, USA
  2. 2School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
  3. 3School of Mathematical Sciences, Jiangxi Science and Technology Normal University, Nanchang 330038, China
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Abstract

Cloud-model hyper-entropy can be overestimated when a scale-inflated subpopulation broadens the tails. We develop a quantile-based estimator that removes location and common scale before recovering cloud shape. Influence normalization balances the selected contrasts, and a prespecified correction addresses centered scale inflation. The theory proves global injectivity of the shape-contrast map for every positive shape ratio, establishes local stability under data and numerical-score perturbations, derives a mixed-rate limit for the singular cloud center, and gives boundary-projected and fixed-positive finite-step limits for the contamination correction. Independently checked numerical integration supports the reference calculations. Simulations and real-data-calibrated semi-synthetic experiments show a clean-sample efficiency cost and improved recovery under moderate scale inflation. A controlled loss ablation attributes the observed gains to the structural construction and weighting rather than active Huber clipping. Benchmark applications illustrate how the estimator can be integrated into a cloud-clustering workflow.

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Cite

BibTeXRIS
BibTeX
@article{cai2026robust,
  title = {{Robust Quantile-Structure Inversion for Cloud Model Parameter Identification}},
  author = {Peiyang Cai and Wenjuan Li and Weidong Rao},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14193577},
  url = {https://www.mdpi.com/2227-7390/14/19/3577},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Robust Quantile-Structure Inversion for Cloud Model Parameter Identification
AU  - Peiyang Cai
AU  - Wenjuan Li
AU  - Weidong Rao
PY  - 2026
DA  - 2026/10/02
JO  - Mathematics
DO  - 10.3390/math14193577
UR  - https://www.mdpi.com/2227-7390/14/19/3577
AB  - Cloud-model hyper-entropy can be overestimated when a scale-inflated subpopulation broadens the tails. We develop a quantile-based estimator that removes location and common scale before recovering cloud shape. Influence normalization balances the selected contrasts, and a prespecified correction addresses centered scale inflation. The theory proves global injectivity of the shape-contrast map for every positive shape ratio, establishes local stability under data and numerical-score perturbations, derives a mixed-rate limit for the singular cloud center, and gives boundary-projected and fixed-positive finite-step limits for the contamination correction. Independently checked numerical integration supports the reference calculations. Simulations and real-data-calibrated semi-synthetic experiments show a clean-sample efficiency cost and improved recovery under moderate scale inflation. A controlled loss ablation attributes the observed gains to the structural construction and weighting rather than active Huber clipping. Benchmark applications illustrate how the estimator can be integrated into a cloud-clustering workflow.
SN  - 2227-7390
ER  -