Fonctions de repartition a n dimensions et leurs marges

By M. Sklar. 1959

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes (2019, background): “Sklar’s theorem [28] states that any joint cumulative distribution F admits a representation in terms of its univariate marginals Fi and a copula function C, F (z1, .”
A mixed copula model for insurance claims and claim sizes (2012, methodology): “Then, by applying Sklar’s theorem (Sklar 1959), a joint distribution function for Yi1 and Yi2 can be constructed as F (yi1, yi2|μi1, ν, μi2, ρ) = C(ui1, ui2|ρ) = Φ2{Φ(ui1),Φ(ui2)|Γ}, (2.3) where ui1 := G1(yi1|μi1, ν2) and ui2 := G2(yi2|μi2). Φ(·) denotes the (univariate) standard normal cdf, while Φ”
Aggregation Functions: A Guide for Practitioners (2007, background): “The problem of the construction of distributions with given marginals can be reduced, thanks to Sklar’s theorem [228], to construction of a copula.”
Multivariate—Intervariable, Spatial, and Temporal—Bias Correction* (2015, methodology): “The basis of the copula approach isSklar’stheorem (Sklar 1959), which states that every multivariate or joint CDF can be expressed by the marginal CDFs of the univariate components of the multivariate random variable and the copula.”
Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index (2005, unknown): “The central result in copula theory is a theorem by Sklar (1959), which states that any continuous N -dimensional cumulative distribution function F , evaluated at point x = (x1, ..., xN) (5) can be represented as F (x) = C(F1(x1), ..., FN(xN)) (1) (4) See Campa and Chang (1998) for more details on…”
Copulas for finance (2000, unknown): “c (x1, x2) = 1 √ 1− ρ2 exp ( −(1) 2 ( ς(2) 1 + 2ς1ς2 + ς 2 2 1− ρ2 ) + 1 2 ( ς(2) 1 + ς 2 2 )) (80)”
Value-at-risk and expected shortfall in cryptocurrencies’ portfolio: a vine copula–based approach (2019, unknown): “Its attractiveness derives from an early result from Sklar (1959), which stated that, for a random vector X ¼ ðX1; ;XdÞ with joint distribution F and marginals F1; ; Fd, there exists a copula2 function C, such that: Fðx1; ; xdÞ ¼ CðF1ðx1Þ; ; FdðxdÞÞ: (4) Conversely, also hold that: Cðu1; ; udÞ ¼…”
The shifting dependence dynamics between the G7 stock markets (2018, unknown): “Sklar (1959) introduced copulas, where a d-dimensional vector x = (x1, x2, . . . , xd) ∈ Rd with joint cumulative distribution function (CDF) F ; then, there exists a copula function C : [0, 1]d → [0, 1], such that the multivariate distribution function is written in terms of univariate marginals…”
Absolutely Continuous Copulas with Given Diagonal Sections (2008, background): “…extendible in a standard way to 2) with univariate marginal distributions: H1L t = HL t 1 = HL t t = C t t = t H2L t = HL 1 t = 2C 1 t −HL t t = 2t − t Because H1L and H 2 L are continuous, in view of Sklar’s Theorem (Sklar, 1959), there exists a unique copula CL such that HL x y = CL x 2y − y .”
A new extension of bivariate FGM copulas (2009, background): “Sklar’s Theorem [29] states that any bivariate distribution with cdf H and marginal cdf F and G can be written H(x, y) = C(F (x),G(y)), where C is a copula.”
Copula-Based Models of Systemic Risk in U.S. Agriculture: Implications for Crop Insurance and Reinsurance Contracts (2015, background): “Though the concept dates back to work by Sklar (1959), copula models have recently realized widespread application in empirical models of joint probability distributions.”