Gábor J. Székely

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The native form of this personal name is Székely J. Gábor. This article uses Western name order when mentioning individuals.
Gábor J. Székely
Born (1947-02-04) 4 February 1947 (age 70)
Budapest, Hungary
Fields Mathematician, Probabilist, Statistician
Institutions National Science Foundation
Hungarian Academy of Sciences
Alma mater Eötvös Loránd University
Doctoral advisor Alfréd Rényi

Gábor J. Székely (Hungarian pronunciation: [ˈseːkɛj], born February 4, 1947 in Budapest) is a Hungarian-American statistician/mathematician best known for introducing the Energy of data[1] [2] [see E-statistics or Package energy in R (programming language)], e.g. the distance correlation[3][4][5] which is a bona fide dependence measure, equals zero exactly when the variables are independent, the distance skewness which equals zero exactly when the probability distribution is diagonally symmetric,[6][7] the E-statistic for normality test[8] and the E-statistic for clustering.[9] Other important discoveries include the Hungarian semigroups,[10][11][12] the location testing for Gaussian scale mixture distributions,[13] the uncertainty principle of game theory,[14] the half-coin [15] which involves negative probability, and the solution of an old open problem of lottery mathematics: in a 5-from-90 lotto the minimum number of tickets one needs to buy to guarantee that at least one of these tickets has (at least) 2 matches is exactly 100.[16]

Life and career[edit]

Székely attended the Eötvös Loránd University, Hungary graduating in 1970. His first advisor was Alfréd Rényi. Székely received his Ph.D. in 1971 from Eötvös Loránd University, the Candidate Degree in 1976 under the direction of Paul Erdős and Andrey Kolmogorov, and the Doctor of Science degree from the Hungarian Academy of Sciences in 1986. Between 1985 and 1995 Székely was the first program manager of the Budapest Semesters in Mathematics. Between 1990 and 1997 he was the founding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest) and editor-in-chief of Matematikai Lapok, the official journal of the János Bolyai Mathematical Society. In 1989 Székely was visiting professor at Yale University, and in 1990-91 he was the first Lukacs Distinguished Professor in Ohio. Székely was academic advisor of Morgan Stanley, NY, and Bunge, Chicago, helped to establish the Morgan Stanley Mathematical Modeling Centre in Budapest (2005) and the Bunge Mathematical Institute (BMI) in Warsaw (2006) to provide quantitative analysis to support the firms' global business. Since 2006 he is a Program Director of Statistics of the National Science Foundation. Székely is also Research Fellow[17] of the Rényi Institute of Mathematics of the Hungarian Academy of Sciences and the author of two monographs, Paradoxes of Probability Theory and Mathematical Statistics, and Algebraic Probability Theory (with Imre Z. Ruzsa).



  • Székely, G. J. (1986) Paradoxes in Probability Theory and Mathematical Statistics, Reidel.
  • Ruzsa, I. Z. and Székely, G. J. (1988) Algebraic Probability Theory, Wiley.
  • Székely, G. J. (editor) (1995) Contests in Higher Mathematics, Springer.
  • Székely, G. J. (1981–82) Why is 7 a mystical number? (in Hungarian) in: MIOK Évkönyv, 482-487, ed. Sándor Scheiber.
  • Székely, G.J. and Ruzsa, I.Z. (1982) Intersections of traces of random walks with fixed sets, Annals of Probability 10, 132-136.
  • Székely, G. J. and Ruzsa, I.Z. (1985) No distribution is prime, Z. Wahrscheinlichkeitstheorie verw. Geb. 70, 263-269.
  • Székely, G. J. and Buczolich, Z. (1989) When is a weighted average of ordered sample elements a maximum likelihood estimator of the location parameter? Advances in Applied Mathematics 10, 439-456. [2]
  • Székely, G. J, Bennett, C.D., and Glass, A. M. W. (2004) Fermat's last theorem for rational exponents, The American Mathematical Monthly 11/4, 322-329.
  • Székely, G. J. (2006) Student's t-test for scale mixtures. Lecture Notes Monograph Series 49, Institute of Mathematical Statistics, 10-18.
  • Székely, G. J., Rizzo, M. L. and Bakirov, N. K. (2007) Measuring and testing independence by correlation of distances, The Annals of Statistics, 35, 2769-2794.PDF
  • Székely, G. J. and Rizzo, M.L. (2009) Brownian distance covariance, The Annals of Applied Statistics, 3/4, 1233-1308.PDF
  • Rizzo, M. L. and Székely, G. J. (2010) DISCO analysis: A nonparametric extension of analysis of variance, The Annals of Applied Statistics, 4/2, 1034-1055.PDF
  • Székely, G.J. and Rizzo, M.L. (2013) Energy statistics: statistics based on distances, Invited paper, Journal of Statistical Planning and Inference, 143/8, 1249-1272.
  • Székely, G.J. and Rizzo, M.L. (2014) Partial distance correlation with methods for dissimilarities, The Annals of Statistics, 42/6, 2382-2412.


  1. ^ E-Statistics: The energy of statistical samples (2002), G.J.Szekely, PDF
  2. ^ G. J. Szekely, M. L. Rizzo (2017) The energy of data, Annual Review of Statistics and Its Application 4(1): 447-479.
  3. ^ Székely, Rizzo and Bakirov (2007)
  4. ^ Székely and Rizzo (2009).
  5. ^ Newton, Michael, A.(2009) Introducing the discussion paper by Székely and Rizzo, Annals of Applied Statistics, 3/4, 1233-1236. PDF
  6. ^ Menshenin, D. O. and Zubkov, A.M.(2008) On the Székely-Móri asymmetry criterion, Austrian Journal of Statistics 37/1, 137-144.
  7. ^ Henze, N.(1997) Limit laws for multivariate skewness in the sense of Móri, Rohatgi and Székely, Statistics&Probability Letters, 33/3, 299-307
  8. ^ Székely, G. J. and Rizzo, M. L. (2005) A new test for multivariate normality, Journal of Multivariate Analysis 93, 58-80.
  9. ^ Székely, G.J. and Rizzo, M. L. (2005) Hierarchical clustering via joint between-within distances: extending Ward’s minimum variance method, Journal of Classification 22 / 2, 151-183.
  10. ^ Székely, G. J. and Ruzsa, I.Z. (1988) Algebraic Probability Theory, Wiley.
  11. ^ Raja, C.R.E. (1999) On a class of Hungarian semigroups and the factorization theorem of Khinchin, J. Theoretical Probability 12/2, 561-569.
  12. ^ Zempléni, A. (1990) On the heredity of Hun and Hungarian property, J. Theoretical Probability 4/3, 599-609.
  13. ^ Székely (2006).
  14. ^ Székely, G. J. and Rizzo, M. L. (2007) The uncertainty principle of game theory, The Americal Mathematical Monthly, 8, 688-702.
  15. ^ Székely, G. J. (2005) Half of a coin: negative probabilities, Wilmott Magazine, July, 66-68.
  16. ^ Z. Füredi, G. J. Székely, and Z. Zubor (1996). "On the lottery problem". Journal of Combinatorial Designs. Wiley. 4 (1): 5–10. doi:10.1002/(sici)1520-6610(1996)4:1<5::aid-jcd2>3.3.co;2-w.  [1] Reprint
  17. ^ Research Fellows of the Rényi Institute of Mathematics.
  18. ^ http://www.amstat.org/careers/fellowslist.cfm
  19. ^ Introducing the new IMS Fellows, IMS Bulletin, 39/6,p.5, 2010.

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