Abe Sklar
Abe Sklar | |
---|---|
Born | |
Died | October 30, 2020 | (aged 94)
Education | University of Chicago California Institute of Technology |
Scientific career | |
Institutions | Illinois Institute of Technology |
Thesis | Summation Formulas Associated with a Class of Dirichlet Series (1956) |
Doctoral advisor | Tom M. Apostol |
Doctoral students | Clark Kimberling Marjorie Senechal |
Abe Sklar (November 25, 1925 – October 30, 2020) was an American mathematician and a professor of applied mathematics at the Illinois Institute of Technology (Illinois Tech) and the inventor of copulas in probability theory.[1]
Education and career
Sklar was born in
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.[4][5] That is, that multivariate cumulative distribution functions can be expressed in terms of copulas.[6] 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.
Bibliography
- Golland, Louise; McGuinness, Brian; Sklar, Abe, eds. (1994). Karl Menger - Reminiscences of the Vienna Circle and the Mathematical Colloquium. Dordrecht: Kluwer Academic Publishers. OCLC 30026523.
- Menger, Karl; Schweizer, Berthold; Sklar, Abe; Sigmund; Schmetterer, Leopold; Gruber, Peter M.; Hlawka, Edmund, eds. (2002). Selecta Mathematica. Volume 1. Vienna. OCLC 1149922502.)
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: CS1 maint: location missing publisher (link - Menger, Karl; Schweizer, Berthold; Sklar, Abe; Sigmund, Karl, eds. (2003). Selecta mathematica. Volume 2. Wien; New York: Springer-Verlag. OCLC 492462474.
- Schweizer, Berthold; Sklar, Abe (2005). Probabilistic metric spaces. Mineola, N.Y. )
References
- ^ Abe Sklar Archived 2019-05-02 at the Wayback Machine, IIT College of Science, retrieved 2019-05-03.
- ^ Abe Sklar at the Mathematics Genealogy Project
- ISSN 2300-2298.
- ^ Fabrizio Durante and Carlo Sempi (2016) Principles of Copula Theory, CRC Press, pp. ix
- ISSN 1939-5108.
- ^ Sklar, A. (1959), "Fonctions de répartition à n dimensions et leurs marges", Publ. Inst. Statist. Univ. Paris (in French), 8: 229–231.