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 Institute of Technology (IIT) is a private research university in Chicago, Illinois. Tracing its history to 1890, the present name was adopted upon the merger of the Armour Institute and Lewis Institute in 1940. The university has prog ...

(IIT) and the inventor of copulas in

probability theory Probability theory 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 expressing it through a set o ...

Education and career

Sklar was born in

Chicago (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name ...

to Jewish parents who immigrated to the United States from

Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inv ...

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

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

in 1942, when he was only 16. Sklar went on to become a student of

Tom M. Apostol Tom Mike Apostol (August 20, 1923 – May 8, 2016) was an American analytic number theorist and professor at the California Institute of Technology, best known as the author of widely used mathematical textbooks. Life and career Apostol was bor ...

at the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, 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 seq ...

and Marjorie Senechal. 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 Probability theorists American mathematicians People from Chicago {{mathematician-stub