Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Order statistics
HTML articles powered by AMS MathViewer

by S. S. Wilks PDF
Bull. Amer. Math. Soc. 54 (1948), 6-50
References
    1. L. von Bortkiewicz, Variationsbreite und mittlerer Fehler, Berlin Math. Ges. Sitzungsber. vol. 21 (1921) pp. 3-11. 2. L. von Bortkiewicz, Die Variationsbreite beim Gauss’schen Fehlergesetz, Nordisk Statistisk Tidskrift vol. 1 (1922) pp. 11-38, 193-220.
  • A. George Carlton, Estimating the parameters of a rectangular distribution, Ann. Math. Statistics 17 (1946), 355–358. MR 16596, DOI 10.1214/aoms/1177730949
  • Allen T. Craig, On the Distributions of Certain Statistics, Amer. J. Math. 54 (1932), no. 2, 353–366. MR 1506901, DOI 10.2307/2371000
  • Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR 0016588
  • Joseph F. Daly, On the use of the sample range in an analogue of Student’s $t$-test, Ann. Math. Statistics 17 (1946), 71–74. MR 15751, DOI 10.1214/aoms/1177731024
  • H. E. Daniels, The statistical theory of the strength of bundles of threads. I, Proc. Roy. Soc. London Ser. A 183 (1945), 405–435. MR 12388, DOI 10.1098/rspa.1945.0011
  • 8. O. L. Davies and E. S. Pearson, Methods of estimating from samples the population standard deviations, Journal of the Royal Statistical Society Supplement vol. 1 (1934) pp. 76-93.
  • W. J. Dixon, A criterion for testing the hypothesis that two samples are from the same population, Ann. Math. Statistics 11 (1940), 199–204. MR 2760, DOI 10.1214/aoms/1177731914
  • Edward Lewis Dodd, The greatest and the least variate under general laws of error, Trans. Amer. Math. Soc. 25 (1923), no. 4, 525–539. MR 1501258, DOI 10.1090/S0002-9947-1923-1501258-4
  • G. Elfving, The asymptotical distribution of range in samples from a normal population, Biometrika 34 (1947), 111–119. MR 19281, DOI 10.1093/biomet/34.1-2.111
  • 12. R. A. Fisher, On the random sequence, Quarterly Journal of the Royal Meteorological Society vol. 52 (1926) p. 250. 13. R. A. Fisher, Coefficient of racial likeness and the future of craniometry, Journal of the Royal Anthropological Institute vol. 66 (1936) pp. 57-63. 14. R. A. Fisher and L. H. C. Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proc. Cambridge Philos. Soc. vol. 24 (1298) pp. 180-190. 15. Maurice Fréchet, Sur la loi de probabilité de l’écart maximum, Annales de la Société Polonaise de Mathématique vol. 6 (1927) (printed in 1928) pp. 92-116. 16. M. Friedman, The use of ranks to avoid the assumption of normality, Journal of the American Statistical Association vol. 32 (1937) pp. 675-701. 17. E. J. Gumbel, Les valeurs extrêmes des distributions statistiques, Annales de l’Institut Henri Poincaré vol. 4 (1935) pp. 115-158. 18. E. J. Gumbel, Les intervalles extrêmes entre les émissions radioactives, Journal de Physique (7) vol. 8 (1937) pp. 321-329, 446-452.
  • E. J. Gumbel, The return period of flood flows, Ann. Math. Statistics 12 (1941), 163–190. MR 4457, DOI 10.1214/aoms/1177731747
  • E. J. Gumbel, Ranges and midranges, Ann. Math. Statistics 15 (1944), 414–422. MR 11418, DOI 10.1214/aoms/1177731211
  • E. J. Gumbel, On the independence of the extremes in a sample, Ann. Math. Statistics 17 (1946), 78–81. MR 15749, DOI 10.1214/aoms/1177731026
  • E. J. Gumbel, The distribution of the range, Ann. Math. Statistics 18 (1947), 384–412. MR 22331, DOI 10.1214/aoms/1177730387
  • E. S. Pearson, The probability integral of the range in samples of $n$ observations from a normal population. I. Foreword and tables, Biometrika 32 (1942), 301–308. MR 6641, DOI 10.1093/biomet/32.3-4.301
  • H. O. Hartley, The range in random samples, Biometrika 32 (1942), 334–348. MR 6653, DOI 10.1093/biomet/32.3-4.334
  • Cecil Hastings Jr., Frederick Mosteller, John W. Tukey, and Charles P. Winsor, Low moments for small samples: A comparative study of order statistics, Ann. Math. Statistics 18 (1947), 413–426. MR 22335, DOI 10.1214/aoms/1177730388
  • 26. H. Hotelling and M. R. Pabst, Rank correlation and tests of significance involving no assumptions of normality, Ann. Math. Stat. vol. 7 (1936) pp. 29-43. 27. J. O. Irwin, The further theory of Francis Galton’s individual difference problem. Biometrika vol. 17 (1925) pp. 100-128. 28. M. G. Kendall, A new measure of rank correlation, Biometrika vol. 30 (1938) pp. 81-93.
  • M. G. Kendall and B. Babington Smith, The problem of $m$ rankings, Ann. Math. Statistics 10 (1939), 275–287. MR 128, DOI 10.1214/aoms/1177732186
  • 30. A. Kolmogoroff, Sulla determinatione empirica di una legge di distributione, Giornale dell’Instituto Italiano degli Attuari vol. 4 (1933) pp. 83-91.
  • A. Kolmogoroff, Confidence limits for an unknown distribution function, Ann. Math. Statistics 12 (1941), 461–463. MR 6684, DOI 10.1214/aoms/1177731684
  • Harold C. Mathisen, A method of testing the hypothesis that two samples are from the same population, Ann. Math. Statistics 14 (1943), 188–194. MR 9285, DOI 10.1214/aoms/1177731460
  • 33. A. T. McKay and E. S. Pearson, A note on the distribution of range in sample sizes of n, Biometrika vol. 25 (1933) pp. 415-420. 34. A. T. McKay, Distribution of the difference between the extreme observations and the sample mean in samples of n from a normal universe, Biometrika vol. 27 (1935) pp. 466-471. 35. R. von Mises, La distribution de la plus grande de n valeurs, Revue de l’Union Interbalkanique vol. 1 (1936) pp. 1-20.
  • A. M. Mood, The distribution theory of runs, Ann. Math. Statistics 11 (1940), 367–392. MR 3493, DOI 10.1214/aoms/1177731825
  • A. M. Mood, On the joint distribution of the medians in samples from a multivariate population, Ann. Math. Statistics 12 (1941), 268–278. MR 5563, DOI 10.1214/aoms/1177731709
  • Frederick Mosteller, Note on an application of runs to quality control charts, Ann. Math. Statistics 12 (1941), 228–232. MR 4453, DOI 10.1214/aoms/1177731753
  • Frederick Mosteller, On some useful “inefficient” statistics, Ann. Math. Statistics 17 (1946), 377–408. MR 19896, DOI 10.1214/aoms/1177730881
  • Frederick Mosteller, A $k$-sample slippage test for an extreme population, Ann. Math. Statistics 19 (1948), 58–65. MR 24116, DOI 10.1214/aoms/1177730290
  • K. R. Nair, The median in tests by randomization, Sankhyā 4 (1940), 543–550. MR 7241
  • K. R. Nair, Table of confidence interval for the median in samples from any continuous population, Sankhyā 4 (1940), 551–558. MR 7589
  • 43. E. G. Olds, Distribution of sums of squares of rank differences for small numbers of individuals, Ann. Math. Stat. vol. 9 (1938) pp. 133-148.
  • P. S. Olmstead, Distribution of sample arrangements for runs up and down, Ann. Math. Statistics 17 (1946), 24–33. MR 15692, DOI 10.1214/aoms/1177731019
  • Paul S. Olmstead and John W. Tukey, A corner test for association, Ann. Math. Statistics 18 (1947), 495–513. MR 23025, DOI 10.1214/aoms/1177730341
  • Edward Paulson, A note on tolerance limits, Ann. Math. Statistics 14 (1943), 90–93. MR 8322, DOI 10.1214/aoms/1177731496
  • E. S. Pearson, Alternative tests for heterogeneity of variance: Some Monte Carlo results, Biometrika 53 (1966), 229–234. MR 198603, DOI 10.1093/biomet/53.1-2.229
  • E. S. Pearson, The probability integral of the range in samples of $n$ observations from a normal population. I. Foreword and tables, Biometrika 32 (1942), 301–308. MR 6641, DOI 10.1093/biomet/32.3-4.301
  • E. S. Pearson, The probability integral of the range in samples of $n$ observations from a normal population. I. Foreword and tables, Biometrika 32 (1942), 301–308. MR 6641, DOI 10.1093/biomet/32.3-4.301
  • E. S. Pearson and H. O. Hartley, Tables of the probability integral of the Studentized range, Biometrika 33 (1943), 88–99. MR 10948, DOI 10.2307/2333622
  • 51. Karl Pearson, Note on Francis Galton’s problem, Biometrika vol. 1 (1902) pp. 390-399. 52. Karl Pearson, On further methods of determining correlation, Drapers’ Company Research Memoirs, Biometric Series IV, Galton Laboratory, London, 1907. 53. Karl Pearson, On the probable errors of frequency constants, Biometrika vol. 13 (1920) pp. 113-132.
  • Karl Pearson (ed.), Tables of the incomplete beta-function, Published for the Biometrika Trustees by Cambridge University Press, London, 1968. Originally prepared under the direction of and edited by Karl Pearson; Second edition with a new introduction by E. S. Pearson and N. L. Johnson. MR 0226815
  • 55. E. J. G. Pitman, Significance tests which may be applied to samples from any populations, Journal of the Royal Statistical Society Supplement vol. 4 (1937) pp. 119-130. 56. E. J. G. Pitman, Significance tests which may be applied to samples from any populations, II. The correlation coefficient test, Journal of the Royal Statistical Society Supplement vol. 4 (1937) pp. 225-232. 57. E. J. G. Pitman, Significance tests which may be applied to samples from any populations, III. The analysis of variance test, Biometrika vol. 29 (1938) pp. 322-335.
  • Herbert Robbins, On distribution-free tolerance limits in random sampling, Ann. Math. Statistics 15 (1944), 214–216. MR 10365, DOI 10.1214/aoms/1177731286
  • 59. S. R. Savur, The use of the median in tests of significance, Proceedings of the Indian Academy of Sciences (Section A) vol. 5 (1937) pp. 564-576.
  • Henry Scheffé, Statistical inference in the non-parametric case, Ann. Math. Statistics 14 (1943), 305–332. MR 9837, DOI 10.1214/aoms/1177731355
  • H. Scheffé and J. W. Tukey, A formula for sample sizes for population tolerance limits, Ann. Math. Statistics 15 (1944), 217. MR 10366, DOI 10.1214/aoms/1177731287
  • H. Scheffé and J. W. Tukey, Non-parametric estimation. I. Validation of order statistics, Ann. Math. Statistics 16 (1945), 187–192. MR 12404, DOI 10.1214/aoms/1177731119
  • 63. W. A. Shewhart, Statistical method from the viewpoint of quality control, U. S. Department of Agriculture, Washington, 1939. 64. N. Smirnoff, Sur la dépendance des members d’un série de variations, Bull. Math. Univ. Moscow vol. 1 (1937-1938) pp. 1-12. 65. N. Smirnoff, Uber die verteilung das allgemeinen Gliedes in der variationsreche, Metron vol. 12 (1935) pp. 59-81. 66. N. Smirnoff, On the estimation of the discrepancy between empirical curves of distribution for two independent samples, Bull. Math. Univ. Moscow vol. 2 (1939).
  • N. Smirnoff, Sur les écarts de la courbe de distribution empirique, Rec. Math. N.S. [Mat. Sbornik] 6(48) (1939), 3–26 (Russian, with French summary). MR 0001483
  • 68. W. L. Stevens, Distribution of groups in a sequence of alternatives, Annals of Eugenics vol. 9 (1939) pp. 10-17.
  • Frieda S. Swed and C. Eisenhart, Tables for testing randomness of grouping in a sequence of alternatives, Ann. Math. Statistics 14 (1943), 66–87. MR 7970, DOI 10.1214/aoms/1177731494
  • 70. William R. Thompson, On confidence ranges for the median and other expectation distributions for populations of unknown distribution form, Ann. Math. Stat. vol. 7 (1936) pp. 122-128. 71. William R. Thompson, Biological applications of normal and range associated significance tests in ignorance of original distribution forms, Ann. Math. Stat. vol. 9 (1938) pp. 281-287. 72. L. H. C. Tippett, On the extreme individuals and the range of samples taken from a normal population, Biometrika vol. 17 (1925) pp. 264-387.
  • John W. Tukey, Non-parametric estimation. II. Statistically equivalent blocks and tolerance regions–the continuous case, Ann. Math. Statistics 18 (1947), 529–539. MR 23033, DOI 10.1214/aoms/1177730343
  • Abraham Wald, Setting of tolerance limits when the sample is large, Ann. Math. Statistics 13 (1942), 389–399. MR 7593, DOI 10.1214/aoms/1177731536
  • Abraham Wald, An extension of Wilks’ method for setting tolerance limits, Ann. Math. Statistics 14 (1943), 45–55. MR 7965, DOI 10.1214/aoms/1177731491
  • 76. A. Wald and J. Wolfowitz, Confidence limits for continous distribution functions, Ann. Math. Stat. vol. 10 (1939) pp. 105-118.
  • A. Wald and J. Wolfowitz, On a test whether two samples are from the same population, Ann. Math. Statistics 11 (1940), 147–162. MR 2083, DOI 10.1214/aoms/1177731909
  • A. Wald and J. Wolfowitz, Note on confidence limits for continuous distribution functions, Ann. Math. Statistics 12 (1941), 118–119. MR 4447, DOI 10.1214/aoms/1177731793
  • A. Wald and J. Wolfowitz, An exact test for randomness in the non-parametric case based on serial correlation, Ann. Math. Statistics 14 (1943), 378–388. MR 9838, DOI 10.1214/aoms/1177731358
  • 80. W. A. Wallis, The correlation ratio for ranked data, Journal of the American Statistical Association vol. 34 (1939) pp. 533-538.
  • John E. Walsh, Some significance tests based on order statistics, Ann. Math. Statistics 17 (1946), 44–52. MR 15753, DOI 10.1214/aoms/1177731021
  • 82. John E. Walsh, Some significance tests for the mean using the sample range and midrange, to appear in Ann. Math. Stat. vol. 19 (1948). 83. B. L. Welch, On the z-test in randomized blocks and Latin squares, Biometrika vol. 29 (1937) pp. 21-52. 84. B. L. Welch, On tests of homogeneity, Biometrika vol. 30 (1938) pp. 149-158.
  • S. S. Wilks, Determination of sample sizes for setting tolerance limits, Ann. Math. Statistics 12 (1941), 91–96. MR 4451, DOI 10.1214/aoms/1177731788
  • S. S. Wilks, Statistical prediction with special reference to the problem of tolerance limits, Ann. Math. Statistics 13 (1942), 400–409. MR 7592, DOI 10.1214/aoms/1177731537
  • S. S. Wilks, Mathematical Statistics, Princeton University Press, Princeton, N.J., 1943. MR 0008657
  • J. Wolfowitz, Additive partition functions and a class of statistical hypotheses, Ann. Math. Statistics 13 (1942), 247–279. MR 7238, DOI 10.1214/aoms/1177731566
  • H. Levene and J. Wolfowitz, The covariance matrix of runs up and down, Ann. Math. Statistics 15 (1944), 58–69. MR 9823, DOI 10.1214/aoms/1177731314
  • L. C. Young, On randomness in ordered sequences, Ann. Math. Statistics 12 (1941), 293–300. MR 5580, DOI 10.1214/aoms/1177731711
Additional Information
  • Journal: Bull. Amer. Math. Soc. 54 (1948), 6-50
  • DOI: https://doi.org/10.1090/S0002-9904-1948-08936-4
  • MathSciNet review: 0025122