Abe Sklar (November 25, 1925 – October 30, 2020) was an American mathematician and a professor of applied mathematics at the

Illinois Institute of Technology The Illinois Institute of Technology, commonly referred to as Illinois Tech and IIT, is a Private university, private research university in Chicago, Illinois, United States. Tracing its history to 1890, the present name was adopted upon the m ...

(Illinois Tech) and the inventor of copulas in

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

Education and career

Sklar was born in

Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...

to Jewish parents who immigrated to the United States from

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

. He attended Von Steuben High School and later enrolled at the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

in 1942, when he was only 16. Sklar went on to become a student of Tom M. Apostol at the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

, where he earned his Ph.D. in 1956. His students at IIT have included geometers

Clark Kimberling Clark Kimberling (born November 7, 1942, in Hinsdale, Illinois) is a mathematician, musician, and composer. He has been a mathematics professor since 1970 at the University of Evansville. His research interests include triangle centers, integer se ...

and

Marjorie Senechal Marjorie Lee Senechal (née Wikler, born 1939) is an American mathematician and historian of science, the Louise Wolff Kahn Professor Emerita in Mathematics and History of Science and Technology at Smith College and editor-in-chief of ''The Mathem ...

. In 1959, Sklar introduced the notion of and the name of " copulas" into

and proved the theorem that bears his name, Sklar's theorem. That is, that multivariate cumulative distribution functions can be expressed in terms of copulas.. 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

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References

1925 births 2020 deaths 20th-century American mathematicians 21st-century American mathematicians American people of Ukrainian-Jewish descent California Institute of Technology alumni Illinois Institute of Technology faculty University of Chicago alumni American probability theorists American mathematicians Mathematicians from Chicago {{mathematician-stub