Random variables, joint distribution functions, and copulas

By A. Sklar. 1973

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Citations in the corpus

A bivariate Weibull count model for forecasting association football scores (2017, methodology): “The power of using a copula approach for modelling dependence comes from a theorem due to Sklar (Sklar, 1973) that states that the joint cumulative distribution function F of any pair of random variables (Y1, Y2) may be written in the form F (y1, y2) = C(F1(y1), F2(y2)), (y1, y2) ∈ 2, where F1 and ”
Stochastic frontier models with dependent error components (2008, methodology): “The modelling technique used here derives from a representation theorem due to Sklar (see Sklar, 1959, 1973) in which the joint distribution of random variables can be expressed as a function of its univariate margins: that function being the copula.”
Rearrangement inequalities for functionals with monotone integrands (2005, background): “Since the lemma follows from Sklar’s outline in [29] rather than from the statement of the theorem, we include its proof for the convenience of the reader.”
Copula Modeling: An Introduction for Practitioners (2007, background): “According to Schweizer (1991), the theorem underlying copulas was introduced in a 1959 article by Sklar written in French; a similar article written in English followed in 1973 (Sklar, 1973).”
Applications of Copulas to Analysis of Efficiency of Weather Derivatives as Primary Crop Insurance Instruments (2004, methodology): “To summarize, the use of copula allows the separation of univariate randomness (defined by the individual probability distribution functions of financial random variables) and dependence structure defined by the copula (Sklar, 1973).”
Copula Theory: An Introduction (2010, background): “The proof of Sklar’s theorem was not given in [191], but a sketch of it was provided in [192] (see also [184]), so that for a few years practitioners in the field had to reconstruct it relying on the hand–written notes by Sklar himself; this was the case, for instance, of the second author.”
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis (2011, unknown): “Sklar’s theorem [34] ensures that for any distribution function F (x1, x2) with marginal distributions F1(x1) and F2(x2), F has the copula representation,”
A Note on Directional Dependence in Regression Setting (2005, background): “Sklar (1973) shows that any multivariate distribution function, say F , can be represented as a function of its marginals, say FX and FY , by using a copula C, i.e., F x y = C FX x FY y .”