On the multivariate probability integral transformation

By Christian Genest, Louis‐Paul Rivest. 2001

203 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e10b61e9e8efe96de49b18082996bde793985542

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Citations in the corpus

Multivariate multiparameter extreme value models and return periods: A copula approach (2010, methodology): “[14] Finally, below we shall also use the Kendall’s distribution (or measure) function KC:I → I [Genest and Rivest, 1993, 2001] given by KC tð Þ ¼ PfW tg ¼ PfC U1; . . . ;Udð Þ tg; ð3Þ where t 2 I is a probability level, W = C(U1, …, Ud) is a univariate r.v. taking value on I, and the Ui’s are…”
Modeling the spatial dependence of floods using the Fisher copula (2019, methodology): “The F-madograms computed for the different simulated samples were compared to the F-madogram of the observations.”
Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask (2007, methodology): “For additional information about the BIPIT and its properties and applications, refer to Genest and Rivest 2001 and Nelsen et al. 2003.”
On the return period and design in a multivariate framework (2011, methodology): “Later we shall use the Kendall’s distribution (or measure ) function K C : I → I (Genest and Rivest, 1993, 2001) given by where t ∈ I is a probability level, W = C (U 1 , ..., U d ) is a uni-variate random variable (hereinafter, r.v. ) taking value on I , and the U i ’s are Uniform r.v.s on I with…”
Detecting Dependence With Kendall Plots (2003, background): “…one has ¬ µ ¬ ¤ ) C ¬ ¿ K C ¬ ¤ ; The American Statistician, November 2003, Vol. 57, No. 4 279 as can be readily checked using the closed-form expression K ¬ (w) = w + w ¬ (1 ¡ w ¬ ) ; 0 µ w µ 1 which derives from the Archimedean character of C ¬ (Genest and MacKay 1986; Genest and Rivest 2001).”
Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall (2010, methodology): “The transformed variables are then called U and V, and this transformation can be expressed as follows [Genest and Rivest, 2001]:”
Enjoy the Joy of Copulas: With a Package copula (2007, methodology): “Wu, Valdez, and Sherris (2006) recently proposed an algorithm for sampling from exchangeable Archimedean copulas based on an extension of the variable transformation technique from the bivariate case to multivariate case (Genest and Rivest 2001).”
Goodness-of-fit Procedures for Copula Models Based on the Integral Probability Transformation (2003, methodology): “In this paper, therefore, a simpler approach is proposed which is rooted in the multivariate probability integral transformation of H ( Genest & Rivest, 2001 ), defined by”
A method to obtain new copulas from a given one (2005, methodology): “Acknowledgements I whish to thank to Christian Genest and Louis-Paul Rivest for bringing reference [ 3 ] to my attention.”
On the properties of some nonparametric concordance measures in the discrete case (2005, result): “In particular, these results complement the recent studies by Genest and Rivest [5], where probability integral transforms are investigated for random pairs with continuous marginals.”
Inference in multivariate Archimedean copula models (2011, background): “is the Kendall distribution function (Barbe et al. 1996; Genest and Rivest 2001; Nelsen et al. 2003).”
On the continuity of center-outward distribution and quantile functions (2018, background): “Indeed, the ranks induced by its empirical counterpart do not enjoy the properties that make traditional (univariate) ranks a successful tool of inference, while the corresponding quantile function—in the Lebesgue-absolutely continuous case, the inverse of the distribution function—does not exhibit ”
Kendall distribution functions (2003, background): “This function also appears in Genest and Rivest (2001) and Nelsen et al. (2001) as a bivariate probability integral transform.”
Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds (2008, background): “The most direct multivariate analogue of the PIT fails in that it is not uniform, even if the observation is drawn from the predictive distribution (Genest and Rivest 2001).”
Hierarchical Kendall copulas: Properties and inference (2012, background): “as rst studied in Genest and Rivest (1993) in the bivariate case and in more detail in Barbe et al. (1996). Other accounts on it can be found, e.g., in Imlahi et al. (1999), Chakak and Imlahi (2001), Genest and Rivest (2001) and Nelsen et al. (2003) as well as in the copula goodness-of-t literature ”