Z. W. Birnbaum

Z. W. Birnbaum
Born	Zygmunt Wilhelm Birnbaum (1903-10-18)October 18, 1903 Lemberg, Austria-Hungary
Died	December 15, 2000(2000-12-15) (aged 97) Seattle, Washington, United States
Other names	Bill Birnbaum
Citizenship	American
Alma mater	University of Lwów University of Göttingen
Known for	Birnbaum-Marshall inequality Birnbaum–Orlicz space Birnbaum–Saunders distribution nonparametric tests
Awards	Guggenheim Fellowship Wilks Memorial Award
Scientific career
Fields	Statistics, Mathematics
Institutions	University of Washington, Seattle
Doctoral advisor	Hugo Steinhaus
Other academic advisors	Edmund Landau Felix Bernstein

Zygmunt Wilhelm "Z. W." Birnbaum (18 October 1903 – 15 December 2000), often known as Bill Birnbaum, 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.

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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 University of Göttingen, Germany from 1929 to 1931, first working as an assistant for Edmund Landau.

After studying insurance mathematics and earning a diploma in actuarial science 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).

• 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. doi:10.4064/sm-3-1-1-67.
• Birnbaum, Z. W. (1948). "On random variables with comparable peakedness". Annals of Mathematical Statistics. 19 (1): 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 (2): 319–327. doi:10.2307/3212003. JSTOR 3212003. MR 0253493. S2CID 120549965.
• 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 (4): 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 (1): 55–77. doi:10.1080/00401706.1961.10489927. JSTOR 1266477. MR 0122658. Archived from the original on September 26, 2017.

• 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. S2CID 121941964.
• 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.

• Z. W. (Bill) (Zygmunt William) Birnbaum at the Mathematics Genealogy Project
• William Birnbaum: MacTutor, mathshistory.st-andrews.ac.uk. Accessed April 16, 2024.
• IMS Past Officials
• Zygmunt William Birnbaum papers 1920–2000, University of Washington
• Zygmunt William Birnbaum photograph collection 1930-1990, University of Washington
• UW Mathematics Dept. Newsletter, Autumn 2001
• Obituary, math.washington.edu via archive.org. Accessed April 16, 2024.
• Photo, Z. W. Birnbaum
• Z. W. Birnbaum, gf.org. Accessed April 16, 2024.
• Samuel S. Wilks Award, amstat.org. Accessed April 16, 2024.