, Volume 21, Issue 1, pp 97–113 | Cite as

Emil J. Gumbel’s last course on the “Statistical theory of extreme values”: a conversation with Tuncel M. Yegulalp

  • Lexuri Fernández
  • Matthias SchererEmail author
Open Access


GUMBEL. Eponym in mathematical statistics for the first type extreme value distribution and the copula that is both of extreme value and Archimedean kind. Hydrologists appreciate Emil J. Gumbel as a pioneer in promoting non-normal distributions in their field. Historians rank him among the most influential German intellectuals of the Weimar Republic. He disclosed secret societies that destabilized the Weimar Republic and used statistical methods to document political murders and to reveal a biased legal system. He was the first professor who lost his position for his political ideals and his stand against the national socialistic party, his books were banned and burned. Stripped of his nationality in 1933 he immigrated to France. In 1940 he escaped to the USA and settled in New York, where he was appointed Adjunct Professor at Columbia University, Department of Industrial Engineering, in 1953. We spoke with Tuncel M. Yegulalp –Professor emeritus of Mining Engineering at Columbia University– about Emil J. Gumbel’s last course on the “Statistical Theory of Extreme Values” back in 1964.


Emil J. Gumbel Extreme value theory History of statistics 

AMS 2000 Subject Classifications

01A60 01A70 60G70 



We would like to thank Tuncel Yegulalp for sharing his time and memories with us. Furthermore, our thanks go to Jose Blanchet for making the contact with Tuncel Yegulalp. Helpful comments on an earlier version of the manuscript were received by Annette Vogt, Thomas Mikosch, Harry Mulgrew, an Associate Editor, and an anonymous referee. We would like to thank Patricia Gumbel and the staff of the Leo Baeck Institute for their overwhelming hospitality during our visit in February 2017.


  1. Brenner, A.D.: Emil J. Gumbel: Weimar German Pacifist and Professor. Studies in Central European History. Brill Academic Publishers, Inc., Boston (2001)Google Scholar
  2. Einstein, A.: The World as I see it. John Lane. The Bodley Head Limited, London (1935)Google Scholar
  3. Fisher, R.A., Tippett, L.H.C.: Limiting forms of the frequency distribution of the largest or smallest member of a sample. Math. Proc. Camb. Philos. Soc. 24(2), 180–190 (1928)CrossRefzbMATHGoogle Scholar
  4. Fréchet, M.: Sur les ensembles compacts de fonctions mesurables. Fundam. Math. 9(1), 25–32 (1927)CrossRefzbMATHGoogle Scholar
  5. Gnedenko, B.: Sur la distribution limite du terme maximum d’une série aléatoire. Ann. Math. 44(3), 423–453 (1943)MathSciNetCrossRefzbMATHGoogle Scholar
  6. Gumbel, E.J.: Über Die Interpolation Des Bevölkerungsstandes. Promotionsschrift. Ludwig Maximiliam Universität, Munich (1914)Google Scholar
  7. Gumbel, E.J.: Die Geschichte eine Plünderung. Freie Zeitung, March 13th, Berlin (1920)Google Scholar
  8. Gumbel, E.J.: Zwei Jahre Mord. Verlag Neues Vaterland, Berlin (1921)Google Scholar
  9. Gumbel, E.J.: Vier Jahre Politischer Mord. Berlin–Fichtenau: Verlag der Neuen Gesellschaft, Berlin (1922)Google Scholar
  10. Gumbel, E.J.: Vom Sinn statistischer Gesetze. Sonderabdruck aus Deutsches Statistisches Zentralbatt (1923)Google Scholar
  11. Gumbel, E.J.: Verschwörer. Malik-Verlag, Vienna (1924)Google Scholar
  12. Gumbel, E.J.: Vom Russland der Gegenwart. E. Laub, Berlin (1927)Google Scholar
  13. Gumbel, E.J.: Abraham Gumbel gestorben. Die Menschenrechte. Berlin, 6. Jg., 15.1 (1931)Google Scholar
  14. Gumbel, E.J.: Das Alter des Methusalem. Zeitschrift für schweizerische Statistik und Volkswirtschschaft 69, 516–530 (1933)Google Scholar
  15. Gumbel, E.J.: Les valeurs extrêmes des distributions statistiques. Annales de l’institut Henri Poincaré, 5(2), 115–158 (1935)MathSciNetzbMATHGoogle Scholar
  16. Gumbel, E.J.: The professor from Heidelberg. In: William, A.N. (ed.) We Escaped: Twelve Personal Narratives of the Flight to America. Macmillan Company (1941)Google Scholar
  17. Gumbel, E.J.: Statistical Theory of Extreme Values and Some Practical Applications. Applied Mathematics Series. US Government Printing Office, Washington (1954)Google Scholar
  18. Gumbel, E.J.: Statistics of Extremes. Columbia University Press, New York and London (1958)zbMATHGoogle Scholar
  19. Gumbel, E.J.: Bivariate exponential distributions. J. Am. Stat. Assoc. 55(292), 698–707 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  20. Gumbel, E.J., Mustafi, C.K.: Comments to: Edward C. Posner, “The application of extreme value theory to error free communication”. Technometrics 8(2), 363–366 (1966)Google Scholar
  21. Gumbel, E.J., Mustafi, C.K.: Some analytical properties of bivariate extremal distributions. J. Am. Stat. Assoc. 62(318), 569–588 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  22. Härdle, W.K., Vogt, A.: Ladislaus von Bortkiewicz–statistician, economist and a European intellectual. Int. Stat. Rev. 83(1), 17–35 (2015)MathSciNetCrossRefGoogle Scholar
  23. Hertz, S.: Emil Julius Gumbel (1891–1966) et la statistique des extrêmes. Ph.D. thesis, Université, Lyon 1 (1997)Google Scholar
  24. Jansen, C.: Emil Julius Gumbel. Porträt Eines Zivilisten. Verlag Das Wunderhorn, Heidelberg (1991)Google Scholar
  25. Layton, C.H.: E. J. Gumbel: Funeral Speech (1966)Google Scholar
  26. Mahtab, M.A., Yegulalp, T.M.: Characterizing jointed rock for tunnel design. In: International Congress on Large Underground Openings, Florence, Italy (1986)Google Scholar
  27. Pfeiffer, K., Rott, J.: Die Erste Ausbürgerungsliste Vom 25. August 1933. Topographie des Terrors. Notizen. Hentrich & Hentrich Verlag, Berlin (2016)Google Scholar
  28. Potter, W.D.: Simplification of the Gumbel Method for Computing Probability Curves. US Department of Agriculture, Soil Conservation Service - Research, Washington D. C. (1949)Google Scholar
  29. Russell, B.: Politische Ideale. Mit Einem Vorwort Von Prof. Albert Einstein. Deutsche Verlagsgesellschaft Für Politic Und Geschichte m.b.H., Berlin. German translation of Political Ideals by E. J. Gumbel (1922)Google Scholar
  30. Russell, B.: Einfürung in Die Matematische Philosophie. Mit Einem Vorwort Von David Hilbert. Drei Masken Verlag, Munich (1923). German translation of Introduction to Mathematical Philosophy by W. Gordon and E. J. GumbelGoogle Scholar
  31. Smirnov, N.V.: Limit distributions for the terms of a variational series. Trudy Matematicheskogo Instituta imeni VA Steklova 25, 3–60 (1949)MathSciNetGoogle Scholar
  32. van Elteren, P.h.: Handleiding Voor Het Gebruik Van Gumbel-papier. Report S 119 (M47). Statistics Department at Center of Mathematics, Amsterdam (1953)Google Scholar
  33. Vogt, A.: Emil Julius Gumbel. Auf Der Suche Nach Wahrheit. Dietz Verlag, Berlin (1991)Google Scholar
  34. Vogt, A.: Emil Julius Gumbel: der erste Herausgeber der mathematischen Manuskripte von Karl Marx. MEGA-Studien 1995(2), 26–41 (1996)Google Scholar
  35. von Bortkiewicz, L.: Variationsbreite Und Mittlerer Fehler. Berliner Mathematische Gesellschaft, Berlin (1921)zbMATHGoogle Scholar
  36. Yegulalp, T.M.: Forecasting for largest earthquakes. Manag. Sci. 21(4), 418–421 (1974)CrossRefGoogle Scholar
  37. Yegulalp, T.M., Kim, K.: Statistical assessment of scale effect on rock properties using the theory of extremes. Trans. Soc. Min. Eng. AIME (1994)Google Scholar
  38. Yegulalp, T.M., Kuo, J.T.: Statistical prediction of the occurrence of maximum magnitude earthquakes. Bull. Seismol. Soc. Am. 64(2), 393–414 (1974)Google Scholar
  39. Yegulalp, T.M., Mahtab, M.A.: A proposed model for statistical representation of mechanical properties of rock. In: The 24th US Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association (1983)Google Scholar
  40. Yegulalp, T.M., Mahtab, M.A., Wane, M.T.: Statistical procedures for characterizing rock properties. In: Proceedings on International Symposium on Application of Rock Characterization Techniques in Mine Design. Society of Mining Engineers (1986)Google Scholar
  41. Yegulalp, T.M., Wane, M.T.: Extreme value statistics improve forecasts of rock behavior. Journal of Mining Engineering 21(8), 79 (1969)Google Scholar

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Authors and Affiliations

  1. 1.Lehrstuhl für FinanzmathematikTechnische Universität MünchenGarching bei MünchenGermany

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