Biography:Abe Sklar
Abe Sklar | |
|---|---|
| Born | November 25, 1925 Chicago , Illinois, USA |
| Died | October 30, 2020 (aged 94) Chicago , Illinois, USA |
| 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 Chicago to Jewish parents who immigrated to the United States from Ukraine . He attended Von Steuben High School and later enrolled at the University of Chicago in 1942, when he was only 16. Sklar went on to become a student of Tom M. Apostol at the California Institute of Technology, where he earned his Ph.D. in 1956. His students at IIT have included geometers Clark Kimberling and Marjorie Senechal.[2][3]
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, ed (1994). Karl Menger - Reminiscences of the Vienna Circle and the Mathematical Colloquium. Dordrecht: Kluwer Academic Publishers. ISBN 0-7923-2711-X. OCLC 30026523. https://www.worldcat.org/oclc/30026523.
- Menger, Karl, ed (2002). Selecta Mathematica. Volume 1. Vienna. ISBN 978-3-7091-6110-4. OCLC 1149922502. https://www.worldcat.org/oclc/1149922502.
- Menger, Karl, ed (2003) (in English). Selecta mathematica. Volume 2. Wien; New York: Springer-Verlag. ISBN 978-3-211-83834-1. OCLC 492462474. https://www.worldcat.org/oclc/492462474.
- Schweizer, Berthold; Sklar, Abe (2005). Probabilistic metric spaces. Mineola, N.Y.. ISBN 978-0-486-14375-0. OCLC 873840651. https://www.worldcat.org/oclc/873840651.
References
- ↑ Abe Sklar , IIT College of Science, retrieved 2019-05-03.
- ↑ Abe Sklar at the Mathematics Genealogy Project
- ↑ Genest, Christian (2021-01-01). "A tribute to Abe Sklar" (in en). Dependence Modeling 9 (1): 200–224. doi:10.1515/demo-2021-0110. ISSN 2300-2298.
- ↑ Fabrizio Durante and Carlo Sempi (2016) Principles of Copula Theory, CRC Press, pp. ix
- ↑ Größer, Joshua; Okhrin, Ostap (2022). "Copulae: An overview and recent developments" (in en). WIREs Computational Statistics 14 (3). doi:10.1002/wics.1557. ISSN 1939-5108.
- ↑ Sklar, A. (1959), "Fonctions de répartition à n dimensions et leurs marges" (in French), Publ. Inst. Statist. Univ. Paris 8: 229–231.
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