Abe Sklar

Abe Sklar
Born(1925-11-25)November 25, 1925
Chicago, Illinois, USA
DiedOctober 30, 2020(2020-10-30) (aged 94)
Chicago, Illinois, USA
EducationUniversity of Chicago
California Institute of Technology
Scientific career
InstitutionsIllinois Institute of Technology
ThesisSummation Formulas Associated with a Class of Dirichlet Series (1956)
Doctoral advisorTom M. Apostol
Doctoral studentsClark 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; McGuinness, Brian; Sklar, Abe, eds. (1994). Karl Menger - Reminiscences of the Vienna Circle and the Mathematical Colloquium. Dordrecht: Kluwer Academic Publishers. ISBN 0-7923-2711-X. OCLC 30026523.
  • Menger, Karl; Schweizer, Berthold; Sklar, Abe; Sigmund; Schmetterer, Leopold; Gruber, Peter M.; Hlawka, Edmund, eds. (2002). Selecta Mathematica. Volume 1. Vienna. ISBN 978-3-7091-6110-4. OCLC 1149922502.{{cite book}}: 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. ISBN 978-3-211-83834-1. OCLC 492462474.
  • Schweizer, Berthold; Sklar, Abe (2005). Probabilistic metric spaces. Mineola, N.Y. ISBN 978-0-486-14375-0. OCLC 873840651.{{cite book}}: CS1 maint: location missing publisher (link)

References

  1. ^ Abe Sklar Archived 2019-05-02 at the Wayback Machine, IIT College of Science, retrieved 2019-05-03.
  2. ^ Abe Sklar at the Mathematics Genealogy Project
  3. ^ Genest, Christian (2021-01-01). "A tribute to Abe Sklar". Dependence Modeling. 9 (1): 200–224. doi:10.1515/demo-2021-0110. ISSN 2300-2298.
  4. ^ Fabrizio Durante and Carlo Sempi (2016) Principles of Copula Theory, CRC Press, pp. ix
  5. ^ Größer, Joshua; Okhrin, Ostap (2022). "Copulae: An overview and recent developments". WIREs Computational Statistics. 14 (3). doi:10.1002/wics.1557. ISSN 1939-5108.
  6. ^ Sklar, A. (1959), "Fonctions de répartition à n dimensions et leurs marges", Publ. Inst. Statist. Univ. Paris (in French), 8: 229–231.


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