Abe Sklar


Abe Sklar was an American mathematician and a professor of applied mathematics at the Illinois Institute of Technology.[1] Born on November 25, 1925, he died on October 30, 2020, at the age of 94.

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.[2] That is, that multivariate cumulative distribution functions can be expressed in terms of copulas.[3] 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.[4]


  1. ^ Abe Sklar, IIT College of Science, retrieved 2019-05-03.
  2. ^ Fabrizio Durante and Carlo Sempi (2016) Principles of Copula Theory, CRC Press, pp. ix
  3. ^ Sklar, A. (1959), "Fonctions de répartition à n dimensions et leurs marges", Publ. Inst. Statist. Univ. Paris (in French), 8: 229–231.
  4. ^ Abe Sklar at the Mathematics Genealogy Project