Notes sur les propriétés des fonctions de répartition empiriques

M. D. Indjoudjian

Revue de Statistique Appliquée (1970)

  • Volume: 18, Issue: 2, page 5-29
  • ISSN: 0035-175X

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Indjoudjian, M. D.. "Notes sur les propriétés des fonctions de répartition empiriques." Revue de Statistique Appliquée 18.2 (1970): 5-29. <http://eudml.org/doc/105886>.

@article{Indjoudjian1970,
author = {Indjoudjian, M. D.},
journal = {Revue de Statistique Appliquée},
language = {fre},
number = {2},
pages = {5-29},
publisher = {Société de Statistique de France},
title = {Notes sur les propriétés des fonctions de répartition empiriques},
url = {http://eudml.org/doc/105886},
volume = {18},
year = {1970},
}

TY - JOUR
AU - Indjoudjian, M. D.
TI - Notes sur les propriétés des fonctions de répartition empiriques
JO - Revue de Statistique Appliquée
PY - 1970
PB - Société de Statistique de France
VL - 18
IS - 2
SP - 5
EP - 29
LA - fre
UR - http://eudml.org/doc/105886
ER -

References

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  1. [1] Andersen, E. Sparre (1949 - "On the number of positive sums of random variables " [Skand. Aktuarietidskrift, 32, pp. 27-36]. Zbl0041.45006MR32115
  2. [2] Anderson, T.W. and Darling, D.A. (1952) - "Asymptotic theory of certain goodness of fit criteria based on stochastic processes ". [Ann. Math. Stat., 23, pp. 193-212]. Zbl0048.11301MR50238
  3. [3] Anderson, T.W. and Darling, D.A. (1954) - "A test of goodness of fit" [J. Am. Stat. Ass., 49, pp. 765-769]. Zbl0059.13302MR69459
  4. [4] Birnbaum, Z. (1952) - "Numerical tables of the distribution of Kolmogorov's statistics for finite sample size" [J. Am. Stat. Ass., 47, pp. 425-444]. Zbl0047.38103MR50826
  5. [5] Birnbaum, Z. and Pyke, R. (1958) - "On some distributions related to the statistics D+n" [Ann. Math. Stat., 29, pp. 179-187]. Zbl0089.14803MR93873
  6. [6] Birnbaum, Z. and Tingey, F.H. (1951) - "One sided confidence contours for probability distribution functions" [Ann. Math. Stat., 22, pp. 592-596]. Zbl0044.14601MR44081
  7. [7] Chapman, D.G. (1958) - "A comparative study of several one-sided goodness of fit tests" [Ann. Math. Stat., 29, pp. 655-673]. Zbl0086.12702MR109398
  8. [8] Cheng, P. (1958) - "Non negative jump points of an empirical distribution function relative to a theoretical distribution function" (en chinois, [traduit dans "Selected Transl. in Math. Stat. and Prob"., IMS and AMS*, vol. 3 (1962). ] Zbl0171.39803MR155377
  9. [9] Darling, D.A. (1957) - "The Kolmogorov-Smirnov, Cramér-von Mises tests" [Ann. Math. Stat., 28, pp. 823- 838]. Zbl0082.13602MR93870
  10. [10] Doob, J.L. (1949) - "Heuristic approach to Kolmogoro-Smirnov theorems [Ann. Math. Stat., 20, pp. 393- 403]. Zbl0035.08901MR30732
  11. [11] Durbin, J. (1961) - "Some methods of constructing exact tests" [Biometrika, 48, pp. 41-55]. Zbl0111.15703MR126313
  12. [12] Feller, W. (1959) - "On combinatorial methods in fluctuation theory " [in "Probability and Statistics ", the Harald Cramér volume, edited by H Grenander, J. Wiley, New York]: Zbl0201.50202MR107884
  13. [13] Feller, W. (1968) - "An introduction to probability theory and its applications" vol. 1, [J. Wiley, 3rd edon]. Zbl0039.13201MR228020
  14. [14] Feller, W. (1966) - "An introduction to probability theory and its applications" vol. 2, [J. Wiley] . Zbl0138.10207MR210154
  15. [15] Gnedenko, B.V. (1952) - "Some results on the maximum discrepancy between two empirical distributions" [Sel. Transl., vol. 1, 1961]. Zbl0112.11007MR116424
  16. [16] Gnedenko, B.V. and Korolyuk, V.S. (1951) - "On the maximum discrepancy between two empirical distributions" [Sel. Transl., vol. 1, 1961]. Zbl0112.11006MR116418
  17. [17] Gnedenko, B.V. and Mihalevič, V.S. (1952) - " On the distribution of the number of excesses of one distribution function over another" [Sel. transl., vol. 1, 1961)] Zbl0112.11102
  18. [18] Gnedenko, B.V. and Mihalevič, V.S. (1953) - " Two theorems on the behaviour of empirical distribution functions " [Sel. transl., vol. 1, 1961).] Zbl0112.11101
  19. [19] Gnedenko, B.V. and Rvačeva, E.L. (1952) - " On a problem of the comparison of two empirical distributions" [Sel. Transl., vol. 1, 1961]. Zbl0112.11104MR116421
  20. [20] Kac, M. (1949) - "On deviations between theoretical and empirical distributions" [Proc. Nat. Acad. Sc., U.S.A., 35, pp. 252- 257]. Zbl0033.19303MR29490
  21. [21] Kac, M., Kiefer, J. and Wolfowitz, J. (1955) - "On tests of normality and other goodness of fit tests on distance méthods" [Ann. Math. Stat., 29, pp. 655- 673]. Zbl0066.12301
  22. [22] Korolyuk, V.S. (1955) - "On the discrepancy of empirical distribution functions for the case of two independant samples " [Sel. transl., vol. 4, 1963]. Zbl0168.17801
  23. [23] Lewis, P.A.W. (1961) - "Distribution of the Anderson-Darling statistic" [Ann. Math. Stat., 32, pp. 1118-1123]. Zbl0201.52305MR131916
  24. [24] Marshall, A.W. (1950) - "The samll sample distribution of n ω2n" [Ann. Math. Stat., 29, pp. 307-309]. Zbl0086.35103
  25. [25 ] Massey, F.J. (1950) - "A note on the power of a non-parametric test" [Ann. Math. Stat., 20, pp. 440- 445]. Zbl0039.14702MR36488
  26. [26] Massey, F.J. (1951) - "The Kolmogorov-Smirnov test of goodness of fit" [J. Ann. Stat. Ass., 46, pp. 68- 78]. Zbl0042.14403
  27. [27] Massey, F.J. (1952) - "Correction to Massey (1950" [Ann. Math. Stat., 23, pp. 637-638]. MR50851
  28. [28] Mihalevič, V.S. (1952) - "On the mutual discrepancy of two empirical distribution functions" [Sel. transl., vol. 1, 1961]. Zbl0112.11103
  29. [29] Miller, L.H. (1956) - "Tables of percentage points of Kolmogorov statistics" [J. Am. Stat. Ass., 51, pp. 111- 121]. Zbl0071.13301MR77063
  30. [30] Owen, D.B. (1962) - "Handbook of statistical tables" [Addison Wesley, Reading (Mass. ] Zbl0102.35203MR161401
  31. [31] Pearson, E.S. and Stephens, M.A. (1962) - "The goodness of fit tests based on W and W[Biometrika, 49, pp. 397-402]. Zbl0221.62015MR166879
  32. [32] Renyi, A. (1966) - "Calcul des probabilités" [Dunod, Paris] Zbl0141.14702MR202161
  33. [33] Smirnov, N.V. (1939) - "On the estimation of the discrepancy between empirical curves of distributions for two independant samples" [Byull. Moskov. Gos. Univ. Sect. A2 - n° 2]. Zbl0023.24902JFM65.1356.04
  34. [34] Smirnov, N.V. (1949) - "On the Cramér-von Mises criterion" [Uspehi Matem. Nauk. (NS), 4, pp. 196- 197]. MR32168
  35. [35] Spitzer, F. (1956) - "A combinatorial lemma and its applications to probability theory" [Transact. Amer. Math. Soc., 82, pp. 323-339]. Zbl0071.13003MR79851
  36. [36] Takacs, L. (1967) - "Combinatorial methods in the theory of stochastic processes" [J. Wiley, New York]. Zbl0162.21303MR217858
  37. [37] Bickel, P.J. (1968) - "Some contribution to the theory of order statistics " (A paraître). 
  38. [38] Bickel, P.J. (1968) - "A distribution - free version of the smirnov Fwo-sample test in the p-variate case" (A paraître). Zbl0179.48704
  39. [39] Billingsley, P.C. (1968) - "Convergence of probability measures" [J. Wiley, New York] . Zbl0172.21201MR233396
  40. [40] Blackman, J. (1956) - "An extension of the Kolmogorov distributionAnn. Math. Stat., 27, pp. 513- 520 + Correction : [Ann. Math. Stat., 29, pp. 318-324).] Zbl0116.10704MR82751
  41. [41] Blum, J.R. Kiefer, J. and Rosenblatt, M. (1961) - "Distribution free tests of independance based on the sample distribution function" [Ann. Math. Stat., 32, pp. 485-498]. Zbl0139.36301MR125690
  42. [42] Capon, J. (1961) - "Asymptotic efficiency of certain locally most powerful rank tests" [Ann. Math. Stat., 32, pp. 88-100] Zbl0107.13703MR120739
  43. [42 bis] Capon, J. (1961) - "Asymptotic efficiency of certain locally most powerful rank tests" [J. Amer. Stat. Ass., 60, pp. 843-853]. Zbl0135.19601MR185758
  44. [43] Carnal, H. (1962) - "Sur les théorèmes de Kolmogorov et Smirnov dans le cas d'une distribution discontinue" [Comm. Math. Helveltici, 37, pp. 19-35]. Zbl0116.37503MR154311
  45. [44] Carvalho, P.E.O. (1959) - "On the distribution of the Kolmogorov-Smirnov Statistic" - [Ann. Math. Stat., 30, pp. 173-176]. Zbl0099.34702MR100942
  46. [45] Chentsov, N.N. (1956) - "Weak convergence of stochastic processes whose trajectories have no discontinuities of the second king and the "heuristic" approach to the Kolmogorov-Smirnov tests" [Theor. Probability Appl., 1, pp. 140-144]. 
  47. [46] Chibisov, D.M. (1965) - "An investigation of the asymptotic power of the tests of fit" [Theor. Probability Appl., 10, pp. 421-437]. Zbl0139.37302MR191025
  48. [47 ] David, H.T. (1958) - "A three-sample Kolmogorov-Smirnov test" [Ann. Math. Stat., 21, pp. 488-506]. Zbl0089.14901MR93871
  49. [48 ] Donsker, M.D. (1952) - "Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems " [Ann. Math. Stat., 22, pp. 277-281]. Zbl0046.35103MR47288
  50. [49] Drion, E.F. (1952) - "Some distribution-free tests for the difference between two empirical distribution functions" [Ann. Math. Stat., 23, pp. 563-574]. Zbl0047.38202MR51492
  51. [50 ] Fisz, M. (1960) - "On a result by M. Rosenblatt concerning the von-Mises Smirnov test" [Ann. Math. Stat., 31, pp. 427- 429]. Zbl0105.33803MR121918
  52. [51] Fisz. M. (1960) - "Some non-parametric tests for the k-sample problem " [colloquium math.7, pp. 289-296]. Zbl0094.14001MR112222
  53. [52] Gnedenko, B.V. (1954) - "Tests of homogeneity of probability distributions in two independant samples" (en russe) [Math. Nachrichten, 12, pp. 29-66]. Zbl0058.34304MR65875
  54. [52 bis] Hajek, J. and Sidak, Z. - "Theory of rank tests" [Acad. press, New York and Acad. publishing house of the Czechoslovak Academy of sc., Prague]. Zbl0161.38102MR229351
  55. [53] Hoeffding, W. (1951) - "A combinatorial central limit theorem" [Ann. Math. Stat., 22, pp. 558-566]. Zbl0044.13702MR44058
  56. [54] Ishii, G. (1958) - "Kolmogorov-Smirnov test in life test [Ann. Inst. Stat. Math.10, pp. 37-38]. Zbl0085.13401MR100331
  57. [55] Kamat, A.R. (1956) - "A two-sample distribution free test" [Biometrika, 43, pp. 377-387]. Zbl0074.13404MR83870
  58. [56] Karlin, S. (1966) - "A first course in stochastic processes" [Acad. press.New York - Chapitre 9 - ] MR208657
  59. [57] Kiefer, J. (1959) - "k-sample analogues of the Kolmogorov-Smirnov and Cramér-von Mises tests" [Ann. Math. Stat., 30, pp. 42 à 447]. Zbl0134.36707MR102882
  60. [58] Motto, M. (1957) - "On the Hoeffding's combinatorial central limit theorem" [Ann. Inst. Stat. Math., 8, pp. 145- 154]. Zbl0084.13802MR89560
  61. [59] Noether, G.E. (1963) - "Note on the Kolmogorov statistic in the discrete case" [Metrika, 7, pp. 115- 116]. Zbl0115.36702MR158462
  62. [60] Rosenblatt, M. (1952) - "Limit theorems associated with variants of the von Mises Statistic" [Ann. Math. Stat.23, pp. 617 -623]. Zbl0048.36003MR52732
  63. [61] Schmid, P. (1958) - "On the Kolmogorov-Smirnov limit theorems for discontinuous functions" [Ann. Math. Stat., 29, pp. 1011-1027]. Zbl0094.13205MR101582
  64. [62] Tsao, C.K. (1954) - "An extension of Massey's distribution of the maximum deviation between two sample cumulative step functions" [Ann. Math. Stat., 25, pp. 587-592]. Zbl0058.35201MR64355
  65. [63 ] Tukey, J.W. (1959) - "A quick, compact, Fwo-sample test to Duckworth's specifications" [Technometrics, 1, pp. 31- 48]. MR106527

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