Biography:Abe Sklar

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Short description: American mathematician (1925–2020)
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

References

  1. Abe Sklar , 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" (in en). 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" (in en). 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" (in French), Publ. Inst. Statist. Univ. Paris 8: 229–231 .