Notes sur les propriétés des fonctions de répartition empiriques
Revue de Statistique Appliquée, Tome 18 (1970) no. 2, pp. 5-29. 
@article{RSA_1970__18_2_5_0,
     author = {Indjoudjian, M. D.},
     title = {Notes sur les propri\'et\'es des fonctions de r\'epartition empiriques},
     journal = {Revue de Statistique Appliqu\'ee},
     pages = {5--29},
     publisher = {Soci\'et\'e de Statistique de France},
     volume = {18},
     number = {2},
     year = {1970},
     language = {fr},
     url = {http://www.numdam.org/item/RSA_1970__18_2_5_0/}
}
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Indjoudjian, M. D. Notes sur les propriétés des fonctions de répartition empiriques. Revue de Statistique Appliquée, Tome 18 (1970) no. 2, pp. 5-29. http://www.numdam.org/item/RSA_1970__18_2_5_0/

[1] Andersen, E. Sparre (1949 - "On the number of positive sums of random variables " [Skand. Aktuarietidskrift, 32, pp. 27-36]. | MR | Zbl

[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]. | MR | Zbl

[3] Anderson, T.W. and Darling, D.A. (1954) - "A test of goodness of fit" [J. Am. Stat. Ass., 49, pp. 765-769]. | MR | Zbl

[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]. | MR | Zbl

[5] Birnbaum, Z. and Pyke, R. (1958) - "On some distributions related to the statistics D+n" [Ann. Math. Stat., 29, pp. 179-187]. | MR | Zbl

[6] Birnbaum, Z. and Tingey, F.H. (1951) - "One sided confidence contours for probability distribution functions" [Ann. Math. Stat., 22, pp. 592-596]. | MR | Zbl

[7] Chapman, D.G. (1958) - "A comparative study of several one-sided goodness of fit tests" [Ann. Math. Stat., 29, pp. 655-673]. | MR | Zbl

[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). ] | MR | Zbl

[9] Darling, D.A. (1957) - "The Kolmogorov-Smirnov, Cramér-von Mises tests" [Ann. Math. Stat., 28, pp. 823- 838]. | MR | Zbl

[10] Doob, J.L. (1949) - "Heuristic approach to Kolmogoro-Smirnov theorems [Ann. Math. Stat., 20, pp. 393- 403]. | MR | Zbl

[11] Durbin, J. (1961) - "Some methods of constructing exact tests" [Biometrika, 48, pp. 41-55]. | MR | Zbl

[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]: | MR | Zbl

[13] Feller, W. (1968) - "An introduction to probability theory and its applications" vol. 1, [J. Wiley, 3rd edon]. | MR | Zbl

[14] Feller, W. (1966) - "An introduction to probability theory and its applications" vol. 2, [J. Wiley] . | MR | Zbl

[15] Gnedenko, B.V. (1952) - "Some results on the maximum discrepancy between two empirical distributions" [Sel. Transl., vol. 1, 1961]. | MR | Zbl

[16] Gnedenko, B.V. and Korolyuk, V.S. (1951) - "On the maximum discrepancy between two empirical distributions" [Sel. Transl., vol. 1, 1961]. | MR | Zbl

[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)] | Zbl

[18] Gnedenko, B.V. and Mihalevič, V.S. (1953) - " Two theorems on the behaviour of empirical distribution functions " [Sel. transl., vol. 1, 1961).] | Zbl

[19] Gnedenko, B.V. and Rvačeva, E.L. (1952) - " On a problem of the comparison of two empirical distributions" [Sel. Transl., vol. 1, 1961]. | MR | Zbl

[20] Kac, M. (1949) - "On deviations between theoretical and empirical distributions" [Proc. Nat. Acad. Sc., U.S.A., 35, pp. 252- 257]. | MR | Zbl

[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]. | Zbl

[22] Korolyuk, V.S. (1955) - "On the discrepancy of empirical distribution functions for the case of two independant samples " [Sel. transl., vol. 4, 1963]. | Zbl

[23] Lewis, P.A.W. (1961) - "Distribution of the Anderson-Darling statistic" [Ann. Math. Stat., 32, pp. 1118-1123]. | MR | Zbl

[24] Marshall, A.W. (1950) - "The samll sample distribution of n ω2n" [Ann. Math. Stat., 29, pp. 307-309]. | Zbl

[25 ] Massey, F.J. (1950) - "A note on the power of a non-parametric test" [Ann. Math. Stat., 20, pp. 440- 445]. | MR | Zbl

[26] Massey, F.J. (1951) - "The Kolmogorov-Smirnov test of goodness of fit" [J. Ann. Stat. Ass., 46, pp. 68- 78]. | Zbl

[27] Massey, F.J. (1952) - "Correction to Massey (1950" [Ann. Math. Stat., 23, pp. 637-638]. | MR

[28] Mihalevič, V.S. (1952) - "On the mutual discrepancy of two empirical distribution functions" [Sel. transl., vol. 1, 1961]. | Zbl

[29] Miller, L.H. (1956) - "Tables of percentage points of Kolmogorov statistics" [J. Am. Stat. Ass., 51, pp. 111- 121]. | MR | Zbl

[30] Owen, D.B. (1962) - "Handbook of statistical tables" [Addison Wesley, Reading (Mass. ] | MR | Zbl

[31] Pearson, E.S. and Stephens, M.A. (1962) - "The goodness of fit tests based on W and W[Biometrika, 49, pp. 397-402]. | MR | Zbl

[32] Renyi, A. (1966) - "Calcul des probabilités" [Dunod, Paris] | MR | Zbl

[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]. | JFM | Zbl

[34] Smirnov, N.V. (1949) - "On the Cramér-von Mises criterion" [Uspehi Matem. Nauk. (NS), 4, pp. 196- 197]. | MR

[35] Spitzer, F. (1956) - "A combinatorial lemma and its applications to probability theory" [Transact. Amer. Math. Soc., 82, pp. 323-339]. | MR | Zbl

[36] Takacs, L. (1967) - "Combinatorial methods in the theory of stochastic processes" [J. Wiley, New York]. | MR | Zbl

[37] Bickel, P.J. (1968) - "Some contribution to the theory of order statistics " (A paraître).

[38] Bickel, P.J. (1968) - "A distribution - free version of the smirnov Fwo-sample test in the p-variate case" (A paraître). | Zbl

[39] Billingsley, P.C. (1968) - "Convergence of probability measures" [J. Wiley, New York] . | MR | Zbl

[40] Blackman, J. (1956) - "An extension of the Kolmogorov distribution Ann. Math. Stat., 27, pp. 513- 520 + Correction : [Ann. Math. Stat., 29, pp. 318-324).] | MR | Zbl

[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]. | MR | Zbl

[42] Capon, J. (1961) - "Asymptotic efficiency of certain locally most powerful rank tests" [Ann. Math. Stat., 32, pp. 88-100] | MR | Zbl

[42 bis] Capon, J. (1961) - "Asymptotic efficiency of certain locally most powerful rank tests" [J. Amer. Stat. Ass., 60, pp. 843-853]. | MR | Zbl

[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]. | MR | Zbl

[44] Carvalho, P.E.O. (1959) - "On the distribution of the Kolmogorov-Smirnov Statistic" - [Ann. Math. Stat., 30, pp. 173-176]. | MR | Zbl

[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].

[46] Chibisov, D.M. (1965) - "An investigation of the asymptotic power of the tests of fit" [Theor. Probability Appl., 10, pp. 421-437]. | MR | Zbl

[47 ] David, H.T. (1958) - "A three-sample Kolmogorov-Smirnov test" [Ann. Math. Stat., 21, pp. 488-506]. | MR | Zbl

[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]. | MR | Zbl

[49] Drion, E.F. (1952) - "Some distribution-free tests for the difference between two empirical distribution functions" [Ann. Math. Stat., 23, pp. 563-574]. | MR | Zbl

[50 ] Fisz, M. (1960) - "On a result by M. Rosenblatt concerning the von-Mises Smirnov test" [Ann. Math. Stat., 31, pp. 427- 429]. | MR | Zbl

[51] Fisz. M. (1960) - "Some non-parametric tests for the k-sample problem " [colloquium math. 7, pp. 289-296]. | MR | Zbl

[52] Gnedenko, B.V. (1954) - "Tests of homogeneity of probability distributions in two independant samples" (en russe) [Math. Nachrichten, 12, pp. 29-66]. | MR | Zbl

[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]. | MR | Zbl

[53] Hoeffding, W. (1951) - "A combinatorial central limit theorem" [Ann. Math. Stat., 22, pp. 558-566]. | MR | Zbl

[54] Ishii, G. (1958) - "Kolmogorov-Smirnov test in life test [Ann. Inst. Stat. Math. 10, pp. 37-38]. | MR | Zbl

[55] Kamat, A.R. (1956) - "A two-sample distribution free test" [Biometrika, 43, pp. 377-387]. | MR | Zbl

[56] Karlin, S. (1966) - "A first course in stochastic processes" [Acad. press. New York - Chapitre 9 - ] | MR

[57] Kiefer, J. (1959) - "k-sample analogues of the Kolmogorov-Smirnov and Cramér-von Mises tests" [Ann. Math. Stat., 30, pp. 42 à 447]. | MR | Zbl

[58] Motto, M. (1957) - "On the Hoeffding's combinatorial central limit theorem" [Ann. Inst. Stat. Math., 8, pp. 145- 154]. | MR | Zbl

[59] Noether, G.E. (1963) - "Note on the Kolmogorov statistic in the discrete case" [Metrika, 7, pp. 115- 116]. | MR | Zbl

[60] Rosenblatt, M. (1952) - "Limit theorems associated with variants of the von Mises Statistic" [Ann. Math. Stat. 23, pp. 617 -623]. | MR | Zbl

[61] Schmid, P. (1958) - "On the Kolmogorov-Smirnov limit theorems for discontinuous functions" [Ann. Math. Stat., 29, pp. 1011-1027]. | MR | Zbl

[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]. | MR | Zbl

[63 ] Tukey, J.W. (1959) - "A quick, compact, Fwo-sample test to Duckworth's specifications" [Technometrics, 1, pp. 31- 48]. | MR