Mathematics and Statistics
Eugene Lukacs (1906 - 1987)
Eugene Lukacs was born in Szombathely, Hungary on August 14, 1906. Six weeks after his birth, he was brought to Vienna where he grew up, got his primary and secondary education and studied mathematics at University of Vienna. He took courses with Hans Hahn, Eduard Helly, Walter Meyer, Leopold Vietoris and Wilhelm Wirtinger.
Eugene met his wife to be, Elizabeth Weisz, at the University of Vienna in 1927. She was taking Mathematics and Physics. They were married in 1935.
Eugene's interest in geometry led him to write a Ph.D. dissertation under Walter Meyer. He earned his Ph.D. degree in 1930. Subsequently he took an actuarial degree in 1931.
Due to scarceness of positions at the University, Eugene taught secondary school in Vienna for two years. Then he accepted a position as an actuary at an insurance company. E. Helly and Z.W. Birnbaum were amongst his colleagues. He stayed with the company until 1937 and also taught extension courses in mathematics at the Volkshochschule Wien Volksheim. When Germany annexed Austria in 1938 he decided to emigrate to USA arriving here in February 1939. About the same time many other Jewish statisticians and mathematicians emigrated to the United States. These included Gerhard Tintner, Z.W. Birnbaum, Henry Mann, Oscar Morgenstern and Abraham Wald.
Upon arrival, Eugene renewed his acquaintance with Abraham Wald whom he had met in Vienna. Under Wald's influence Eugene became interested in probability and statistics. Wald introduced him to the vast literature on probability and statistics that was largely unknown in Central Europe at that time. Wald invited him to attend his, and Hotelling's lectures at Columbia. Thus began Eugene's long and fruitful career in statistics during which he wrote five books and well over 100 papers.
Eugene arrived in the USA after the great depression and could not find a suitable position. Lisl had preceded him by three months. She found a position at Garrison High School in Baltimore and encouraged Eugene to seek a position at Friends High School in Baltimore. He was hired to teach Latin and senior level mathematics. He taught there for a short while and then held teaching positions at several colleges. He taught physics and mathematics. In 1945 he joined the faculty at Our Lady of Cincinnati College and remained there until 1953. While there he was stimulated by his association with Otto Szasz and became interested in probability theory. He wrote several papers with Szasz. While on leave from College, he worked as a mathematical statistician at the U.S. Naval Ordinance Test Station in China Lake, California and later at the NBS in Washington D.C. In 1953 Eugene joined ONR and became the head of its Statistics Branch. During his tenure at NBS and ONR he taught at American University in Washington D.C.
In 1955, Eugene joined the Catholic University of America where he organized the Statistical Laboratory in 1959 and became its first and only director. Among members of the group were Edward Batschlet, Tatsuo Kawata, Radha Laha, M. Masuyama and Vijay Rohatgi. Long term visitors included Harald Cramer, Jerzy Neyman, Alfred Renyi, Paul Levy, Kemp de Fariat, Demetrios Kappos, Istvan Vincze, Imre Csiszar, Roger Cuppens, Herman Dinges, Daniel Dugue, Harold Bergstrom, Leopold Schmettrer. Many other prominent statistician such as Sir R.A. Fisher, Mark Kac, Yu. V. Linnik, Paul Erdos, Michael Loeve, David Blackwell, Betty Scott, Jacob Wolfowitz, Jack M. Hemmersley, H. McKean, William Cochran, William Feller, Herbert Robbins, Henri Teicher, Harry Kesten, Yuan Shih Chow, and Janos Aczel made short visits. Lisl found a position at Madeira School for Girls in suburban Washington and taught physics and biology.
On his retirement in 1972, Eugene moved with his colleagues Laha and Rohatgi to Bowling Green where he remained until 1976. He then accepted visiting positions in Vienna and Erlangen. In 1978 he returned to his home in Washington D.C. but continued to travel to international meetings and give talks at various Universities. He continued his research, writing and editing until his death in 1987. Indeed his monograph Developments in Characteristic Function Theory was published in 1983.
Eugene's primary interest was in the theory of characteristic functions. Until the appearance of his celebrated monograph, Characteristic Functions, in 1960 the properties of characteristic functions and their applications appeared in the English language only in textbooks such as those of Cramer, Gnedenko and Kolmogorov, and Loeve. His monograph was the first to present a unified and detailed treatment of the subject. Characteristic Functions is widely quoted and was, in the sixties and seventies, an indispensable book for graduate students and researchers in analytic probability theory. A greatly revised and enhanced second edition was published in 1970 followed by Developments in Characteristics Function Theory in 1983. Characteristic Functions has been translated into German, Russian, French and Chinese and continues to be of great use to analytic probabilists.
Eugene's other interests included characterizations of distributions, robustness (stability) of characterization results and functional equations. We mention two outstanding examples of his work.
- In 1942 Lukacs introduced the so-called method of differential equations in characteristic function theory for the first time to solve problems of characterization of distributions. Using this method he studied the independence of the sample mean and sample variance in the iid case when the population variance was finite. He showed that the independence of statistics and is necessary and sufficient for the common distribution function to be normal. Geary had already proved this celebrated result under the condition that is finite for all . Eugene found the natural proof even though the second moment condition he used in the proof was later eliminated by Kawata, Sakamoto and Zinger. It is interesting to note that the correlation coefficient r between and is zero if and only if the third central moment is zero. On the other hand, the numerical value of r can approach 1 even for distributions concentrated on two points. One can show that a sharp upper bound for |r| for unimodal distributions is .
- In 1955 Eugene gave a nice characterization for the gamma distributions whose density functions have the form
He showed that, if X and Y are independent, nondegenerate, positive rv's, then X + Y and X / Y are independent if and only if X and Y have a gamma distribution with the same scale parameter . This result has many applications. For example we can show that X and Y is multiplicatively infinitely divisible by writing
Eugene served countless committees and councils on behalf of IMS, National Research Council, American Mathematical Society, and American Association for Advancement of Science. He was an associate editor of JASA (1951-55, 1961-63), Annals of Mathematical Statistics (1958-64,1968-70), Journal of Multivariate Analysis (1970-83). Jointly with Z.W. Birnbaum, he was the founding editor of the Academic Press Series in Probability and Statistics (1962-85). He chaired the translation committee of AMS for many years. He received many honors such fellow of IMS, ASA, AAAS, elected member of ISI and Austrian Academy of Science. He was the first professor at BGSU to be given the title of University Professor. A volume of papers dedicated to him on his seventieth birthday was published by the Academic Press in 1981. In 1989 BGSU and the State of Ohio honored him again by funding a visiting professorship named after him.
Eugene had visiting appointments at Sorbonne, Swiss Federal Institute, Institute of Technology, Vienna, Universities of Hull and Sheffield, University of Erlangen-Nurenberg, University of Brussels, University of Athens.
His hobbies and interests included stamp and coin collecting, hiking, bird watching, photography and traveling. His favorite vacation spots were Oberwolfach and his cottage in Viennese Woods. He spent part of his summer at his cottage practically every summer.
Eugene was a constant source of encouragement to his colleagues and students. He received and quickly responded to numerous questions on characteristic functions from researchers all over the world. Indeed we still get letters addressed to him concerning problems in characteristic functions and characterization of distributions.
Professor Lukacs will be remembered not only for his contributions to probability and statistics but also as a friend and a colleague and as a human being of integrity. We honor him every year with the symposium which bears his name.
- J. Gani and V. K. Rohatgi, editors, Contributions to Probability, Academic Press, New York, 1981.
- J. Gani, editor, The Evolution of a Statistician, Springer-Verlag, Berlin, 1982.
- Vijay K. Rohatgi, Eugene Lukacs , J. Applied Probability, 25 (1988), 641-646.
- Vijay K. Rohatgi and Gabor Szekely, Eugene Lukacs, 1906-1987, Aequationes Mathematicae, 38 (1989), 1-8.
- Hermann Witting, A Conversation with Leopold Schmetterer, Statistical Science, 6 (1991), 437-447.
Mrs. Lukacs died at her home in Washington D.C. on November 13, 1993. Lisl and Eugene had no children.
Vijay K. Rohatgi