Zygmunt Wilhelm Birnbaum

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Z. W. (Bill) Birnbaum
Alma materDoctor of PhilosophyUniversity of Lwów
Known forBirnbaum-Marshall inequality
Birnbaum–Orlicz space
Birnbaum–Saunders distribution
nonparametric tests
AwardsPresident of the Institute of Mathematical Statistics
Fellow of the American Statistical Association

Elected member of the International Statistical Institute
Guggenheim Fellowship

Wilks Memorial Award of the American Statistical Association
Scientific career
FieldsStatistics, Mathematics
InstitutionsUniversity of Washington, Seattle
Doctoral advisorHugo Steinhaus
Notable studentsRonald Pyke, Albert Marshall, Sam Saunders
InfluencesWładysław Orlicz
Stanisław Mazur
Stefan Banach

Zygmunt Wilhelm Birnbaum (18 October 1903 – 15 December 2000) was a Polish-American mathematician and statistician who contributed to functional analysis, nonparametric testing and estimation, probability inequalities, survival distributions, competing risks, and reliability theory.

After first earning a law degree and briefly practicing law, Birnbaum obtained his PhD in 1929 at the University of Lwów under the supervision of Hugo Steinhaus, and was associated with the Lwów School of Mathematics. He visited Göttingen, Germany from 1929 to 1931.

After studying insurance mathematics and earning a Versicherungsmathematik Diplom with Felix Bernstein in Göttingen, he worked as an actuary in Vienna during 1931–1932, and was then transferred to Lwów where he continued working as an actuary. After obtaining a position as a correspondent for a Polish newspaper, he arrived in New York as a reporter in 1937. He became a Professor of Mathematics at the University of Washington in 1939 (with help from Harold Hotelling and letters of reference from Richard Courant, Albert Einstein, and Edmund Landau).

Birnbaum was actively involved in reliability work with Boeing through the Boeing Scientific Research Laboratories during the late 1950s and 1960s, and was a key member of the "Seattle school of reliability", a group which also included Tom Bray, Gordon Crawford, James Esary, George Marsaglia, Al Marshall, Frank Proschan, Ron Pyke, and Sam Saunders.

Birnbaum served as Editor of the Annals of Mathematical Statistics (1967–1970) and as President of the Institute of Mathematical Statistics (1964). He received a Guggenheim Fellowship in 1960 (spent at the Sorbonne, Paris), and a Fulbright Program Fellowship in 1964 (spent at the University of Rome).

Selected publications[edit]


  • Introduction to Probability and Mathematical Statistics, 1962, Harper and Brothers.


  • Birnbaum, Z.W.; Orlicz, W. (1931). "Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen" (PDF). Studia Mathematica. 3: 1–67.
  • Birnbaum, Z. W. (1948). "On random variables with comparable peakedness". Annals of Mathematical Statistics. 19: 76–81. doi:10.1214/aoms/1177730293. JSTOR 2236059. MR 0024099.
  • Birnbaum, Z. W.; Marshall, A.W. (1961). "Some multivariate Chebyshev inequalities with extensions to continuous parameter processes". Annals of Mathematical Statistics. 32 (3): 687–703. doi:10.1214/aoms/1177704964. JSTOR 2237830. MR 0148106.
  • Birnbaum, Z. W.; Saunders, S. C. (1969). "A new family of life distributions". Journal of Applied Probability. 6: 319–327. JSTOR 3212003. MR 0253493.
  • Birnbaum, Z. W.; Esary, J. D.; Marshall, A. W. (1966). "A stochastic characterization of wear-out for components and systems". Annals of Mathematical Statistics. 37: 816–825. doi:10.1214/aoms/1177699362. JSTOR 2238571. MR 0193727.
  • Birnbaum, Z. W.; Esary, J. D.; Saunders, S.C. (1961). "Multicomponent systems and structures and their reliability". Technometrics. 3: 55–77. doi:10.1080/00401706.1961.10489927. JSTOR 1266477. MR 0122658.


  • Marshall, Albert W. (1990). "A conversation with Z. William Birnbaum". Statistical Science. 5 (2): 227–241. doi:10.1214/ss/1177012174. MR 1062577.
  • Woyczynski, Wojbor (2001). "Seeking Birnbaum, or nine lives of a mathematician". Mathematical Intelligencer. 23 (2): 36–40. doi:10.1007/bf03026626. MR 1843237.
  • Saunders, Sam C. (1975). "Birnbaum's contributions to reliability theory". Reliability and fault tree analysis (Conf., Univ. California, Berkeley, Calif., 1974). Soc. Indust. Appl. Math., Philadelphia, Pa. pp. xv–xxxix. MR 0424493.

External links[edit]