# An essay on copula modelling for discrete random vectors; or how to pour new wine into old bottles

@article{Geenens2019AnEO, title={An essay on copula modelling for discrete random vectors; or how to pour new wine into old bottles}, author={Gery Geenens}, journal={arXiv: Methodology}, year={2019} }

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not identifiable, which causes serious inconsistencies. In spite of this, downplaying statements are widespread in the related literature, and copula methods are used for…

## Figures from this paper

## 2 Citations

### Quantum Implementation of Risk Analysis-relevant Copulas

- Computer Science
- 2020

It turns out that such a discretized copula can be expressed using simple constructs present in the quantum computing: binary fraction expansion format, comonotone/independent random variables, controlled gates, and convex combinations, and is therefore suitable for a quantum computer implementation.

### The Hellinger Correlation

- MathematicsJournal of the American Statistical Association
- 2020

Abstract In this article, the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones, shown to imply…

## References

SHOWING 1-10 OF 66 REFERENCES

### On rank correlation measures for non-continuous random variables

- Computer Science, Mathematics
- 2007

### A Primer on Copulas for Count Data

- Computer ScienceASTIN Bulletin
- 2007

The authors show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case.

### Discrete Multivariate Analysis: Theory and Practice

- Mathematics
- 1975

Discrete Multivariate Analysis is a comprehensive text and general reference on the analysis of discrete multivariate data, particularly in the form of multidimensional tables, and contains a wealth of material on important topics.

### An Introduction to Copulas

- Computer Science, Economics
- 2016

These notes provide an introduction to modeling with copulas. Copulas are the mechanism which allows us to isolate the dependency structure in a multivariate distribution. In particular, we can…

### Inference for copula modeling of discrete data: a cautionary tale and some facts

- Computer Science
- 2017

Some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data are elucidated and the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models are contrasted.

### Matrix representation of copulas and quasi-copulas defined on non-square grids of the unit square

- Computer ScienceFuzzy Sets Syst.
- 2010

### Association and Estimation in Contingency Tables

- History
- 1968

OUR 1967 Committee on Publications, chaired by David L. Wallace, found that many American Statistical Association members desired more review and survey papers. These have been hard to come by, and…

### Copula in a multivariate mixed discrete-continuous model

- Computer ScienceComput. Stat. Data Anal.
- 2016

### The Hellinger Correlation

- MathematicsJournal of the American Statistical Association
- 2020

Abstract In this article, the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones, shown to imply…