Eugene Lukacs: Difference between revisions

Eugene Lukacs
Eugene Lukacs
	Eugene Lukacs (1906–1987)
Born	14 August 1906; Szombathely, Austria-Hungary
Died	21 December 1987 (aged 81); Washington, D.C.
Alma mater	University of Vienna
Known for	Characteristic Functions, Characterization of Distributions
	Scientific career
Fields	Mathematician, Probabilist, Statistician
Institutions	Catholic University of America ; Bowling Green State University
Doctoral advisor	Walther Mayer

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Eugene Lukacs (Hungarian: Lukács Jenő, 14 August 1906 – 21 December 1987) was a Hungarian-American statistician 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.

Born to a Jewish family in Szombathely,^[3] 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, Walther Mayer, Leopold Vietoris and Wilhelm Wirtinger. In 1930 he earned his doctorate in geometry under the supervision of Walther Mayer, 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.^[4]

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 Loève. 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^[5] appeared in 1970, followed by Developments in Characteristics Function Theory^[6] 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, a Fellow of the American Academy of Arts and Sciences since 1958,^[7] and a Fellow of the American Statistical Association since 1969. In 1973 he was elected to the Austrian Academy of Sciences.

Books

E. Lukacs; R. G. Laha (1964). Applications of Characteristic Functions (Griffin's Statistical Monographs & Courses, No. 14). New York: T. Hafner Pub. Co. p. 202.
E. Lukacs (1970). Characteristic Functions) (second ed.). New York: Hafner Pub. Co.
E. Lukacs (1972). Probability and Mathematical Statistics; An Introduction. New York: Academic Press.
E. Lukacs (1975). Stochastic Convergence. New York: Academic Press.
E. Lukacs (1983). Developments in Characteristic Function Theory. New York: Macmillan.

Journal articles

Laha, R. G.; Lukacs, E. (1977). "On a functional equation which occurs in a characterization problem". Aequationes Mathematicae. 16 (3): 259–274. doi:10.1007/BF01836038. S2CID 122866588.
Beer, S.; Lukacs, E. (1973). "Characterizations of the normal distribution by suitable transformations". Journal of Applied Probability. 10 (1): 100–108. doi:10.2307/3212498. JSTOR 3212498. S2CID 125053197.
Cuppens, R.; Lukacs, E. (1970). "On the domains of definition of analytic characteristic functions". Annals of Mathematical Statistics. 41 (3): 1096–1101. doi:10.1214/aoms/1177696990.
Laha, R. G.; Lukacs, E.; Rényi, A. (1964). "A generalization of a theorem of E. Vincze". Magyar Tud. Akad. Mat. Kutató Int. Közl. 9: 237–239.
Laha, R. G.; Lukacs, E.; Newman, M. (1960). "On the independence of a sample central moment and the sample mean". Annals of Mathematical Statistics. 31 (4): 1028–1033. doi:10.1214/aoms/1177705675.
Laha, R. G.; Lukacs, E. (1960). "On the independence of a sample central moment and the sample mean". Annals of Mathematical Statistics. 31 (4): 1028–1033. doi:10.1214/aoms/1177705675.
Laha, R. G.; Lukacs, E. (1960). "On certain functions of normal variates which are uncorrelated of a higher order". Biometrika. 47 (1/2): 175–176. doi:10.2307/2332969. JSTOR 2332969.
Laha, R. G.; Lukacs, E. (1960). "On a problem connected with quadratic regression". Biometrika. 47 (3–4): 335–343. doi:10.1093/biomet/47.3-4.335.
Lukacs, Eugene (1955). "A characterization of the gamma distribution". Annals of Mathematical Statistics. 26 (2): 319–324. doi:10.1214/aoms/1177728549.
Lukacs, Eugene; King, Edgar P. (1954). "A property of the normal distribution". Annals of Mathematical Statistics. 25 (2): 389–394. doi:10.1214/aoms/1177728796.
Lukacs, Eugene; Szász, Otto (1954). "Nonnegative trigonometric polynomials and certain rational characteristic functions". Journal of Research of the National Bureau of Standards. 52 (3): 153–160. doi:10.6028/jres.052.021.
Lukacs, Eugene; Szász, Otto (1954). "Certain Fourier transforms of distributions. II". Canadian Journal of Mathematics. 6: 186–189. doi:10.4153/CJM-1954-020-5. S2CID 247197222.
Lukacs, Eugene (1952). "The stochastic independence of symmetric and homogeneous linear and quadratic statistics". Annals of Mathematical Statistics. 23 (3): 442–449. doi:10.1214/aoms/1177729389.
Lukacs, Eugene (1942). "A characterization of the normal distribution". Annals of Mathematical Statistics. 13: 91–93. doi:10.1214/aoms/1177731647.

Notes

^ Vijay K. Rohatgi and Gábor J. Székely (1989). "Eugene Lukacs". Aequationes Mathematicae. 38: 1–8. doi:10.1007/BF01839488. S2CID 120104820. (Obituary)
^ E. Lukacs (1960). Characteristic Functions). London: Griffin.
^ O'Connor, John J.; Robertson, Edmund F., "Eugene Lukacs", MacTutor History of Mathematics Archive, University of St Andrews
^ Rohatgi (1988)
^ E. Lukacs (1970). Characteristic Functions) (second ed.). New York: Hafner Pub. Co.
^ E. Lukacs (1983). Developments in Characteristic Function Theory. New York: Macmillan.
^ "Historic Fellows". American Academy of Arts and Sciences (AAAS).(search on "last name=Lukacs")

References

J Gani and V K Rohatgi (eds.), Contributions to Probability (New York, 1981). 2014 pbk reprint
J Gani (ed.), The Evolution of a Statistician (Berlin, 1982).
V K Rohatgi, Obituary: Eugene Lukacs, J. Applied Probability 25 (1988), 641–646. JSTOR 3213993

External links

O'Connor, John J.; Robertson, Edmund F., "Eugene Lukacs", MacTutor History of Mathematics Archive, University of St Andrews

[rohatgi1989-1] Vijay K. Rohatgi and Gábor J. Székely (1989). "Eugene Lukacs". Aequationes Mathematicae. 38: 1–8. doi:10.1007/BF01839488. S2CID 120104820. (Obituary)

[2] E. Lukacs (1960). Characteristic Functions). London: Griffin.

[3] O'Connor, John J.; Robertson, Edmund F., "Eugene Lukacs", MacTutor History of Mathematics Archive, University of St Andrews

[4] Rohatgi (1988)

[CF2-5] E. Lukacs (1970). Characteristic Functions) (second ed.). New York: Hafner Pub. Co.

[Lukacs83-6] E. Lukacs (1983). Developments in Characteristic Function Theory. New York: Macmillan.

[7] "Historic Fellows". American Academy of Arts and Sciences (AAAS).(search on "last name=Lukacs")

[1]

[2]

[3]

[4]

[5]

[6]

[7]

@@ Line 1: / Line 1: @@
+__NOTOC__
-'''Eugene Lukacs''' (14 August 1906 – 21 December 1987) was a [[Hungary|Hungarian]] [[statistician]] born in [[Szombathely]], notable<ref name="rohatgi1989">{{cite journal| doi=10.1007/BF01839488| author=Vijay K. Rohatgi and [[Gabor Szekely|Gábor J. Székely]]|title=Eugene Lukacs| journal=Aequationes Mathematicae| year=1989| volume=38| pages=1&ndash;8}} (Obituary)</ref> for his work in characterization of distributions, stability theory, and being the author of ''Characteristic Functions''<ref> {{Cite book |author=E. Lukacs|title=Characteristic Functions)|location=London|publisher=Griffin|year=1960 |unused_data=.}}</ref>, a classic textbook in the field.
 {{Infobox scientist
-|name              = Lukacs, Eugene
+|name              =  Eugene Lukacs
 |image             = EugeneLukacs2.jpg
-|caption           = Eugene Lukacs (1906 - 1987)
+|caption           = Eugene Lukacs (1906–1987)
 |birth_date        = 14 August 1906
-|birth_place       = [[Szombathely]], [[Hungary]]
+|birth_place       = [[Szombathely]], [[Austria-Hungary]]
-|death_date        = 21 December 1987
+|death_date        = {{d-da|21 December 1987|14 August 1906}}
 |death_place       = [[Washington, D.C.]]
-|fields            = [[Mathematician]], [[Probabilist]], [[Statistician]]
+|fields            = [[Mathematician]], [[Mathematician|Probabilist]], [[Statistician]]
 |workplaces        = [[Catholic University of America]] <br /> [[Bowling Green State University]]
 |alma_mater        = [[University of Vienna]]
-|doctoral_advisor  = Walter Meyer
+|doctoral_advisor  = [[Walther Mayer]]
-|known_for         = Work in Probability Theory, Characteristic Functions, Characterization of Distributions
+|known_for         = [[Characteristic function|Characteristic Functions]], Characterization of Distributions
 }}
+'''Eugene Lukacs''' ([[Hungarian people|Hungarian]]: ''Lukács Jenő'', 14 August 1906 – 21 December 1987) was a Hungarian-American [[statistician]] notable<ref name="rohatgi1989">{{cite journal| doi=10.1007/BF01839488| author=Vijay K. Rohatgi and [[Gabor Szekely|Gábor J. Székely]]|title=Eugene Lukacs| journal=[[Aequationes Mathematicae]]| year=1989| volume=38| pages=1&ndash;8| s2cid=120104820}} (Obituary)</ref> for his work in characterization of distributions, stability theory, and being the author of ''Characteristic Functions'',<ref>{{Cite book |author=E. Lukacs|title=Characteristic Functions)|location=London|publisher=Griffin|year=1960}}</ref> 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.<ref>Rohatgi (1988)</ref>
+Born to a Jewish family in [[Szombathely]],<ref>{{MacTutor|id=Lukacs|title=Eugene Lukacs}}</ref> 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 (mathematician)|Hans Hahn]], [[Eduard Helly]], [[Walther Mayer]], [[Leopold Vietoris]] and [[Wilhelm Wirtinger]]. In 1930 he earned his doctorate in geometry under the supervision of [[Walther Mayer]], 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.<ref>Rohatgi (1988)</ref>
-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.]]
+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.
+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 [[Radha Laha|Laha]] and Rohatgi to [[Bowling Green State University]] in Bowling Green, Ohio, where he remained until 1976.
+On his retirement from Catholic University in 1972, he moved with his colleagues [[Radha Laha|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 function (probability theory)|characteristic function]]s. 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''<ref name=CF2>{{Cite book |author=E. Lukacs|title=Characteristic Functions)|edition=second|location=New York|publisher=Hafner Pub. Co.|year=1970 |unused_data=.}}</ref> appeared in 1970, followed by ''Developments in Characteristics Function Theory''<ref name=Lukacs83>{{Cite book|author=E. Lukacs|title= Developments in Characteristic Function Theory|publisher=Macmillan|location=New York|year=1983|unused_data=.}}</ref> 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]].
+His primary interest was in the theory of [[characteristic function (probability theory)|characteristic function]]s. 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 Loève. 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''<ref name=CF2>{{Cite book |author=E. Lukacs|title=Characteristic Functions)|edition=second|location=New York|publisher=Hafner Pub. Co.|year=1970}}</ref> appeared in 1970, followed by ''Developments in Characteristics Function Theory''<ref name=Lukacs83>{{Cite book|author=E. Lukacs|title= Developments in Characteristic Function Theory|publisher=Macmillan|location=New York|year=1983}}</ref> 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, a Fellow of the [[American Academy of Arts and Sciences]] since 1958,<ref>{{cite web|title=Historic Fellows|website=American Academy of Arts and Sciences (AAAS)|url=https://www.aaas.org/fellows/historic}}(search on "last name=Lukacs")</ref> and a Fellow of the [[American Statistical Association]] since 1969. In 1973 he was elected to the [[Austrian Academy of Sciences]].
 ==Books==
-* {{Cite book |author=E. Lukacs and R. G. Laha|title=Applications of Characteristic Functions (Griffin's Statistical Monographs & Courses, No. 14)|location=New York|publisher=T. Hafner Pub. Co.|year=1964 |pages=202 |unused_data=.}}
+* {{Cite book |author1=E. Lukacs |author2=R. G. Laha |title=Applications of Characteristic Functions (Griffin's Statistical Monographs & Courses, No. 14)|location=New York|publisher=T. Hafner Pub. Co.|year=1964 |pages=202}}
-* {{Cite book |author=E. Lukacs|title=Characteristic Functions)|edition=second|location=New York|publisher=Hafner Pub. Co.|year=1970 |unused_data=.}}
+* {{Cite book |author=E. Lukacs|title=Characteristic Functions)|edition=second|location=New York|publisher=Hafner Pub. Co.|year=1970}}
-* {{Cite book|author=E. Lukacs|title= Probability and Mathematical Statistics; An Introduction |publisher=Academic Press|location=New York|year=1972.}}
+* {{Cite book|author=E. Lukacs|title= Probability and Mathematical Statistics; An Introduction |publisher=Academic Press|location=New York|year=1972}}
-* {{Cite book|author=E. Lukacs|title= Stochastic Convergence |publisher=Academic Press|location=New York|year=1975.}}
+* {{Cite book|author=E. Lukacs|title= Stochastic Convergence |publisher=Academic Press|location=New York|year=1975}}
-* {{Cite book|author=E. Lukacs|title= Developments in Characteristic Function Theory|publisher=Macmillan|location=New York|year=1983|unused_data=.}}
+* {{Cite book|author=E. Lukacs|title= Developments in Characteristic Function Theory|publisher=Macmillan|location=New York|year=1983}}
-== Journal Articles ==
+== Journal articles ==
-* {{Cite journal|unused_data= .|doi= 10.1007/BF01836038|author= Laha, R. G. and Lukacs, E.|year=1977|title= On a functional equation which occurs in a characterization problem|journal=Aequationes Math.|volume=  16|issue= 3|pages= 259–274}}
+* {{Cite journal|doi= 10.1007/BF01836038|author1=Laha, R. G.  |author2=Lukacs, E.|year=1977|title= On a functional equation which occurs in a characterization problem|journal=[[Aequationes Mathematicae]]|volume=  16|issue= 3|pages= 259–274|s2cid=122866588 }}
+* {{Cite journal|doi=10.2307/3212498|author1=Beer, S.  |author2=Lukacs, E.|title=  Characterizations of the normal distribution by suitable transformations|journal= Journal of Applied Probability|volume=  10|issue=1|year=1973|pages= 100–108|jstor=3212498 |s2cid=125053197 }}
-* {{Cite journal|doi=10.2307/3212498|unused_data=.|author=Beer, S. and  Lukacs, E.|title=  Characterizations of the normal distribution by suitable transformations|journal= J. Appl. Probability|volume=  10|issue=1|year=1973|pages= 100–108}}
+* {{Cite journal|doi=10.1214/aoms/1177696990|author1=Cuppens, R.  |author2=Lukacs, E.|title=  On the domains of definition of analytic characteristic functions|journal= Annals of Mathematical Statistics|volume=  41|issue=3 |year=1970|pages= 1096–1101|doi-access=free}}
+* {{Cite journal|author1=Laha, R. G. |author2=Lukacs, E. |author3=Rényi, A. |title=  A generalization of a theorem of E. Vincze|journal= Magyar Tud. Akad. Mat. Kutató Int. Közl.|volume=  9|year=  1964 |pages=237–239}}
-* {{Cite journal|doi=10.1214/aoms/1177696990|unused_data=.|author=Cuppens, R. and  Lukacs, E.|title=  On the domains of definition of analytic characteristic functions|journal= Ann. Math. Statist.|volume=  41|year=1970|pages= 1096–1101}}
+* {{Cite journal|doi=10.1214/aoms/1177705675|author1=Laha, R. G. |author2=Lukacs, E. |author3=Newman, M. |year=1960|title=On the independence of a sample central moment and the sample mean|journal=Annals of Mathematical Statistics|volume=  31|issue=4|pages= 1028–1033|doi-access=free}}
+* {{Cite journal|doi=10.1214/aoms/1177705675|author1=Laha, R. G.  |author2=Lukacs, E.|year=1960|title=On the independence of a sample central moment and the sample mean|journal=Annals of Mathematical Statistics|volume=  31|issue=4 |pages= 1028–1033|doi-access=free}}
-* {{Cite journal|unused_data= .|author= Laha, R. G. and  Lukacs, E. and  Rényi, A.|title=  A generalization of a theorem of E. Vincze|journal= Magyar Tud. Akad. Mat. Kutató Int. Közl.|volume=  9|year=  1964 |pages=237–239}}
+* {{Cite journal|author1=Laha, R. G.  |author2=Lukacs, E.|year=1960|title= On certain functions of normal variates which are uncorrelated of a higher order| journal=Biometrika|volume=  47|issue=1/2|pages=175–176|doi=10.2307/2332969|jstor=2332969}}
+* {{Cite journal|author1=Laha, R. G.  |author2=Lukacs, E.|title=  On a problem connected with quadratic regression |journal=Biometrika  |volume=47 |issue=3–4|year= 1960|pages= 335–343 |doi=10.1093/biomet/47.3-4.335}}
-* {{Cite journal|doi=10.1214/aoms/1177705675|unused_data=.|author=Laha, R. G. and Lukacs, E. and Newman, M.|year=1960|title=On the independence of a sample central moment and the sample mean|journal=Ann. Math. Statist.|volume=  31|pages= 1028–1033}}
+* {{Cite journal|doi= 10.1214/aoms/1177728549|author= Lukacs, Eugene|title=A characterization of the gamma distribution|journal=Annals of Mathematical Statistics|volume=26|issue= 2|year=1955|pages=319–324|doi-access=free}}
+* {{Cite journal|doi= 10.1214/aoms/1177728796|author1=Lukacs, Eugene  |author2=King, Edgar P.|title=A property of the normal distribution|journal=Annals of Mathematical Statistics|volume=25|issue=2 |year=1954|pages=389–394|doi-access=free}}
+* {{Cite journal|author1=Lukacs, Eugene  |author2=Szász, Otto |title=Nonnegative trigonometric polynomials and certain rational characteristic functions|journal= Journal of Research of the National Bureau of Standards|volume=52|issue=3 |year=1954|pages=153–160|doi=10.6028/jres.052.021|doi-access=free}}
-* {{Cite journal|doi=10.1214/aoms/1177705675|unused_data=.|author=Laha, R. G. and Lukacs, E.|year=1960|title=On the independence of a sample central moment and the sample mean|journal=Ann. Math. Statist.|volume=  31|pages= 1028–1033}}
+* {{Cite journal|doi= 10.4153/CJM-1954-020-5|author1=Lukacs, Eugene  |author2=Szász, Otto |title=Certain Fourier transforms of distributions. II|journal=  Canadian Journal of Mathematics|volume=6|year=1954|pages=186–189|s2cid=247197222 |doi-access=free}}
-* {{Cite journal|unused_data=.|author=Laha, R. G. and Lukacs, E.|year=1960|title= On certain functions of normal variates which are uncorrelated of a higher order| journal=Biometrika|volume=  47|pages=175–176}}
+* {{Cite journal|doi= 10.1214/aoms/1177729389|author= Lukacs, Eugene|title=The stochastic independence of symmetric and homogeneous linear and quadratic statistics|journal=Annals of Mathematical Statistics|volume=23|issue= 3|year=1952|pages=442–449|doi-access=free}}
+* {{Cite journal|doi= 10.1214/aoms/1177731647|author= Lukacs, Eugene|title=A characterization of the normal distribution|journal=Annals of Mathematical Statistics|volume=13|year=1942|pages=91–93|doi-access=free}}
-* {{Cite Journal|unused_data= .|author= Laha, R. G. and  Lukacs, E.|title=  On certain functions of normal variates which are uncorrelated of a higher order|journal= Biometrika |volume=47|year=  1960|pages= 175–176}}
-* {{Cite journal|author=Laha, R. G. and  Lukacs, E.|title=  On a problem connected with quadratic regression |journal=Biometrika  |volume=47 |year= 1960|pages= 335–343.}}
-* {{Cite journal|doi= 10.1214/aoms/1177728549|unused_data= .|author= Lukacs, Eugene|title=A characterization of the gamma distribution|journal=Ann. Math. Statist.|volume=26|year=1955|pages=319–324}}
-* {{Cite journal|doi= 10.1214/aoms/1177728796|unused_data= .|author= Lukacs, Eugene and King, Edgar P.|title=A property of the normal distribution|journal=Ann. Math. Statist.|volume=25|year=1954|pages=389–394}}
-* {{Cite journal|unused_data= .|author= Lukacs, Eugene and Szász, Otto |title=Nonnegative trigonometric polynomials and certain rational  characteristic functions|journal= J. Research Nat. Bur. Standards|volume=52|year=1954|pages=153–160}}
-* {{Cite journal|doi= 10.4153/CJM-1954-020-5|unused_data= .|author= Lukacs, Eugene and Szász, Otto |title=Certain Fourier transforms of distributions. II|journal=  Canadian J. Math.|volume=6|year=1954|pages=186–189}}
-* {{Cite journal|doi= 10.1214/aoms/1177729389|unused_data= .|author= Lukacs, Eugene|title=The stochastic independence of symmetric and homogeneous linear and  quadratic statistics|journal=Ann. Math. Statist.|volume=23|year=1952|pages=442–449}}
-* {{Cite journal|doi= 10.1214/aoms/1177731647|unused_data= .|author= Lukacs, Eugene|title=A characterization of the normal distribution|journal=Ann. Math. Statist.|volume=13|year=1942|pages=91–93}}
 ==Notes==
 {{reflist}}
+==See also==
+* [[Lukacs's proportion-sum independence theorem]]
+* [[Lukacs Distinguished Professor|Eugene Lukacs Distinguished Visiting Professor]]
 ==References==
-*J Gani and V K Rohatgi (eds.), Contributions to Probability  (New York, 1981).
+*J Gani and V K Rohatgi (eds.), Contributions to Probability  (New York, 1981). [https://books.google.com/books?id=9qziBQAAQBAJ 2014 pbk reprint]
 *J Gani (ed.), The Evolution of a Statistician  (Berlin, 1982).
-*V K Rohatgi, Obituary: Eugene Lukacs, J. Applied Probability  25 (1988), 641–646.
+*V K Rohatgi, Obituary: Eugene Lukacs, J. Applied Probability  25 (1988), 641–646. {{jstor|3213993}}
-==See also==
+==External links==
+*{{MacTutor Biography|id=Lukacs}}
-[[Lukacs Distinguished Professor|Eugene Lukacs Distinguished Visiting Professor]]
+{{Authority control}}
-{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
-| NAME              = Lukacs, Eugene
-| ALTERNATIVE NAMES =
-| SHORT DESCRIPTION = Scientist
-| DATE OF BIRTH     = 14 August 1906
-| PLACE OF BIRTH    = Szombathely, Hungary
-| DATE OF DEATH     = 21 December 1987
-| PLACE OF DEATH    = Washington, D.C.
-}}
 {{DEFAULTSORT:Lukacs, Eugene}}
+[[Category:20th-century Hungarian mathematicians]]
-[[Category:20th-century mathematicians]]
-[[Category:Hungarian mathematicians]]
 [[Category:1906 births]]
 [[Category:1987 deaths]]
 [[Category:Hungarian statisticians]]
-[[Category:probability theorists]]
+[[Category:Probability theorists]]
+[[Category:Fellows of the American Statistical Association]]
+[[Category:Fellows of the American Academy of Arts and Sciences]]
 [[Category:Fellows of the Institute of Mathematical Statistics]]
 [[Category:Members of the Hungarian Academy of Sciences]]
+[[Category:University of Vienna alumni]]
+[[Category:Catholic University of America faculty]]
-[[de:Eugene Lukacs]]
+[[Category:Bowling Green State University faculty]]
-[[it:Eugene Lukacs]]
+[[Category:Mathematicians from Austria-Hungary]]
+[[Category:Mathematical statisticians]]

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