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PreprintCC BY 4.0arXiv

Quasi-copulas with a prescribed sub-track section

  • Jiehua Xie
  • Wei Zou
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Abstract

In this paper, we consider the quasi-copulas and copulas with a prescribed sub-track section, i.e., with given values along the curve segment connecting the points (x0,0) and (1,1-x0) for 0<x0<1. By employing the technique based on the W-ordinal sum, we provide methods for constructing quasi-copulas and copulas whose sub-track section coincides with a given one. Then, we further investigate construction methods for symmetric quasi-copulas and copulas with a prescribed sub-track section. Furthermore, we determine the best-possible bounds for the class of quasi-copulas sharing a common sub-track section, and verify that the lower bound obtained is also the best-possible lower bound for the class of copulas with a common sub-track section. Finally, we examine several properties of the bound (quasi-)copulas with a prescribed sub-track section, including their comparison with bound (quasi-)copulas with a given track section or a sub-diagonal section, as well as their statistical characteristic and concordance order.

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Cite

BibTeXRIS
BibTeX
@misc{xie2026quasicopulas,
  title = {{Quasi-copulas with a prescribed sub-track section}},
  author = {Jiehua Xie and Wei Zou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01247},
  eprint = {2610.01247},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01247},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quasi-copulas with a prescribed sub-track section
AU  - Jiehua Xie
AU  - Wei Zou
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01247
UR  - https://arxiv.org/abs/2610.01247
AB  - In this paper, we consider the quasi-copulas and copulas with a prescribed sub-track section, i.e., with given values along the curve segment connecting the points (x0,0) and (1,1-x0) for 0<x0<1. By employing the technique based on the W-ordinal sum, we provide methods for constructing quasi-copulas and copulas whose sub-track section coincides with a given one. Then, we further investigate construction methods for symmetric quasi-copulas and copulas with a prescribed sub-track section. Furthermore, we determine the best-possible bounds for the class of quasi-copulas sharing a common sub-track section, and verify that the lower bound obtained is also the best-possible lower bound for the class of copulas with a common sub-track section. Finally, we examine several properties of the bound (quasi-)copulas with a prescribed sub-track section, including their comparison with bound (quasi-)copulas with a given track section or a sub-diagonal section, as well as their statistical characteristic and concordance order.
ER  -