In 1959, Sklar introduced the notion of and the name of "copulas" into probability theory and proved the theorem that bears his name, Sklar's theorem. That is, that multivariate cumulative distribution functions can be expressed in terms of copulas. This representation of distribution functions, which is valid in any dimension and unique when the margins are continuous, is the basis of copula modeling, a widespread data analytical technique used in statistics; this representation is often termed Sklar's representation. Schweizer–Sklar t-norms are also named after Sklar and Berthold Schweizer, who studied them together in the early 1960s.
Sklar was a student of Tom M. Apostol at the California Institute of Technology, where he earned his Ph.D. in 1956. In turn, his students at IIT have included geometers Clark Kimberling and Marjorie Senechal.