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The Joy of Copulas: Bivariate Distributions with Uniform Marginals
Abstract
We describe a class of bivariate distributions whose marginals are uniform on the unit interval. Such distributions are often called “copulas.” The particular copulas we present are especially well suited for use in undergraduate mathematical statistics courses, as many of their basic properties can be derived using elementary calculus. In particular, we show how these copulas can be used to illustrate the existence of distributions with singular components and to give a geometric interpretation to Kendall's tau.
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Citations
Cited by
Understanding Relationships Using Copulas
Frees, E. W., & Valdez, E. A. (1998) · North American Actuarial Journal · doi:10.1080/10920277.1998.10595667 · Cited by 1,257
Statistical Inference Procedures for Bivariate Archimedean Copulas
Genest, C., & Rivest, L.-P. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476372 · Cited by 1,251
Self-citationEstimating the success of re-identifications in incomplete datasets using generative models
Rocher, L., Hendrickx, J. M., & de Montjoye, Y.-A. (2019) · Nature Communications · doi:10.1038/s41467-019-10933-3 · Cited by 816
Multivariate hydrological frequency analysis using copulas
Favre, A., El Adlouni, S., Perreault, L., Thiémonge, N., & Bobée, B. (2004) · Water Resources Research · doi:10.1029/2003wr002456 · Cited by 696
Enjoy the Joy of Copulas: With a Package copula
Yan, J. (2007) · Journal of Statistical Software · doi:10.18637/jss.v021.i04 · Cited by 502
Metadata
- Authors
- Genest, C., & Mackay, J.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1986-11
- Volume
- 40
- Issue
- 4
- Pages
- 280-283
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2049567982
- Cited by
- 790
- References
- 0
- FWCI
- 5.81
- Type
- journal article
- Language
- en
- Open access
- closed
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