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Eugene Lukacs

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Lukacs, Eugene
Eugene Lukacs (1906–1987)
Born14 August 1906
Szombathely, Austria-Hungary
Died21 December 1987
Washington, D.C.
Alma materUniversity of Vienna
Known forWork in Probability Theory, Characteristic Functions, Characterization of Distributions
Scientific career
FieldsMathematician, Probabilist, Statistician
InstitutionsCatholic University of America
Bowling Green State University
Doctoral advisorWalter Meyer

Eugene Lukacs (Hungarian: Lukács Jenő, 14 August 1906 – 21 December 1987) was a Hungarian statistician born in Szombathely, notable[1] for his work in characterization of distributions, stability theory, and being the author of Characteristic Functions,[2] a classic textbook in the field.

From six weeks after birth Lukacs lived in Vienna, Austria. There he received primary and secondary education and studied mathematics at University of Vienna. His professors included Hans Hahn, Eduard Helly, Walter Meyer, Leopold Vietoris and Wilhelm Wirtinger. In 1930 he earned his doctorate in geometry under the supervision of Walter Meyer, and a degree in actuarial science in 1931. Eugene met his future wife Elizabeth Weisz (Lisl) in 1927 at the University of Vienna, and they married in 1935. He taught secondary mathematics for two years and later accepted a position with an insurance company, where Eduard Helly and Z. W. Birnbaum were colleagues. After Germany annexed Austria in 1938, he decided to emigrate to the United States, arriving in 1939.[3]

In 1953 Eugene joined the Office of Naval Research (ONR) USA, and became the director of Statistics. While at ONR he also taught at American University in Washington, D.C.

Lukacs joined the Catholic University of America, Washington, D.C. in 1955. There he organized the Statistical Laboratory in 1959 and became its first and only director. Researchers at the Statistical Laboratory included Edward Batschlet, Tatsuo Kawata, Radha Laha, M. Masuyama and Vijay Rohatgi, and many distinguished visitors.

On his retirement from Catholic University in 1972, he moved with his colleagues Laha and Rohatgi to Bowling Green State University in Bowling Green, Ohio, where he remained until 1976.

His primary interest was in the theory of characteristic functions. Prior to publication of his 1960 monograph, Characteristic Functions, the English language textbooks on the subject were translations of works by Cramer, Gnedenko and Kolmogorov, and Loeve. Lukacs' monograph was the first to present a unified and detailed treatment of the subject, and has remained a classical reference on the subject. The revised and expanded second edition of Characteristic Functions[4] appeared in 1970, followed by Developments in Characteristics Function Theory[5] in 1983. Characteristic Functions has been translated into several languages and continues to be an essential resource on the subject.

Lukacs was an elected Fellow of the Institute of Mathematical Statistics since 1957, and a Fellow of the American Statistical Association since 1969. In 1973 he was elected to the Austrian Academy of Sciences.

Books

  • E. Lukacs and R. G. Laha (1964). Applications of Characteristic Functions (Griffin's Statistical Monographs & Courses, No. 14). New York: T. Hafner Pub. Co. p. 202. {{cite book}}: Unknown parameter |unused_data= ignored (help)
  • E. Lukacs (1970). Characteristic Functions) (second ed.). New York: Hafner Pub. Co. {{cite book}}: Unknown parameter |unused_data= ignored (help)
  • E. Lukacs (1972.). Probability and Mathematical Statistics; An Introduction. New York: Academic Press. {{cite book}}: Check date values in: |year= (help)CS1 maint: year (link)
  • E. Lukacs (1975.). Stochastic Convergence. New York: Academic Press. {{cite book}}: Check date values in: |year= (help)CS1 maint: year (link)
  • E. Lukacs (1983). Developments in Characteristic Function Theory. New York: Macmillan. {{cite book}}: Unknown parameter |unused_data= ignored (help)

Journal articles

  • Laha, R. G. and Lukacs, E. (1977). "On a functional equation which occurs in a characterization problem". Aequationes Math. 16 (3): 259–274. doi:10.1007/BF01836038. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Beer, S. and Lukacs, E. (1973). "Characterizations of the normal distribution by suitable transformations". J. Appl. Probability. 10 (1): 100–108. doi:10.2307/3212498. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Cuppens, R. and Lukacs, E. (1970). "On the domains of definition of analytic characteristic functions". Ann. Math. Statist. 41: 1096–1101. doi:10.1214/aoms/1177696990. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Laha, R. G. and Lukacs, E. and Rényi, A. (1964). "A generalization of a theorem of E. Vincze". Magyar Tud. Akad. Mat. Kutató Int. Közl. 9: 237–239. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Laha, R. G. and Lukacs, E. and Newman, M. (1960). "On the independence of a sample central moment and the sample mean". Ann. Math. Statist. 31: 1028–1033. doi:10.1214/aoms/1177705675. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Laha, R. G. and Lukacs, E. (1960). "On the independence of a sample central moment and the sample mean". Ann. Math. Statist. 31: 1028–1033. doi:10.1214/aoms/1177705675. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Laha, R. G. and Lukacs, E. (1960). "On certain functions of normal variates which are uncorrelated of a higher order". Biometrika. 47: 175–176. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Laha, R. G. and Lukacs, E. (1960). "On a problem connected with quadratic regression". Biometrika. 47: 335–343.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  • Lukacs, Eugene and King, Edgar P. (1954). "A property of the normal distribution". Ann. Math. Statist. 25: 389–394. doi:10.1214/aoms/1177728796. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Lukacs, Eugene and Szász, Otto (1954). "Nonnegative trigonometric polynomials and certain rational characteristic functions". J. Research Nat. Bur. Standards. 52: 153–160. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Lukacs, Eugene and Szász, Otto (1954). "Certain Fourier transforms of distributions. II". Canadian J. Math. 6: 186–189. doi:10.4153/CJM-1954-020-5. {{cite journal}}: Unknown parameter |unused_data= ignored (help)CS1 maint: multiple names: authors list (link)
  • Lukacs, Eugene (1952). "The stochastic independence of symmetric and homogeneous linear and quadratic statistics". Ann. Math. Statist. 23: 442–449. doi:10.1214/aoms/1177729389. {{cite journal}}: Unknown parameter |unused_data= ignored (help)

Notes

  1. ^ Vijay K. Rohatgi and Gábor J. Székely (1989). "Eugene Lukacs". Aequationes Mathematicae. 38: 1–8. doi:10.1007/BF01839488. (Obituary)
  2. ^ E. Lukacs (1960). Characteristic Functions). London: Griffin. {{cite book}}: Unknown parameter |unused_data= ignored (help)
  3. ^ Rohatgi (1988)
  4. ^ E. Lukacs (1970). Characteristic Functions) (second ed.). New York: Hafner Pub. Co. {{cite book}}: Unknown parameter |unused_data= ignored (help)
  5. ^ E. Lukacs (1983). Developments in Characteristic Function Theory. New York: Macmillan. {{cite book}}: Unknown parameter |unused_data= ignored (help)

See also

References

  • J Gani and V K Rohatgi (eds.), Contributions to Probability (New York, 1981).
  • J Gani (ed.), The Evolution of a Statistician (Berlin, 1982).
  • V K Rohatgi, Obituary: Eugene Lukacs, J. Applied Probability 25 (1988), 641–646.

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