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Allgemeiner Bericht über Monte-Carlo-Methoden. (German) Zbl 0171.15304


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[1] Bouckhaert, L.: Les methodes de Monte Carlo. Rev. Questions Sci. (5) 17 (1956), 344–359.
[2] Buslenko, N. P., u.J. A. Schreider: Die Monte-Carlo-Methode. Leipzig 1964. · Zbl 0138.12204
[3] Clark, C. E.: The utility of statistics of random numbers. Oper. Res. 8, 2 (1960), 185–195. · Zbl 0090.11102 · doi:10.1287/opre.8.2.185
[4] Cseke, V.: Sur la méthode Monte Carlo. Gaz. Mat. Fiz. Ser. (A) 13 (66) (1961), 352–360. · Zbl 0101.11704
[5] Dahlquist, G.: The Monte Carlo method. Nordisk. Mat. Tidskr. 2 (1954), 27–43, 80. · Zbl 0056.12201
[6] Dupac, V.: Monte Carlo Methods. Appl. Mat. 7 (1962) 1–20.
[7] Engeler, E.: Über die Monte Carlo Methode. Mitt. Verein. Schweizer Versich.-Math. 58 (1958), 67–76. · Zbl 0080.10903
[8] Filippi, S.: Kleine Einführung in die Monte-Carlo-Methode. Elemente der Mathematik 18, 4 (1963). · Zbl 0114.09703
[9] Forsythe, G. E., H. H. Germond et al.: Monte Carlo Methods. Nat. Bur. Stand. Appl. Math. 12 (1951).
[10] Franckx, E.: La méthode de Monte Carlo. Assoc. Actuar. Belges Bull. 58 (1956), 89–101.
[11] Hammersley, J. M., andD. C. Handscomb: Monte Carlo Methods. London/New York 1964.
[12] Meyer, H. A. (Ed.), andN. Metropolis: Symposium on Monte Carlo Methods. New York 1956.
[13] Metropolis. N.;Ulam, S. – ’The Monte Carlo method’ – Jour. Amer. Stat. Assoc. 44 (1949). 335–342. · Zbl 0033.28807 · doi:10.1080/01621459.1949.10483310
[14] Shreider, Y. A. (Ed.): Method of Statistical Testing – Monte Carlo Method. Amsterdam/London/New York 1964. · Zbl 0192.25609
[15] Ulam, S.: On the Monte Carlo Method. Proc. 2nd Symp. Large-scale Digital Calculating machinery 1951, 207–212.
[16] Clark, C. E., andB. Weber-Holz: Exponentially distributed random numbers. Baltimore 1960. · Zbl 0101.11703
[17] Owen, D. B. – ’Handbook of statistical tables’ – London, Paris 1962. · Zbl 0102.35203
[18] Quenouille, M. H.: Tables of Random Observations from standard Distributions. Biometrika 46 (1959), 178–202. · Zbl 0087.14001 · doi:10.1093/biomet/46.1-2.178
[19] Rand Corp.: A million random digits and 100000 normal deviates. Glencoe, Illinois, 1955.
[20] Sengupta, J. M., andN. Bhattacharya: Tables of random normal deviates. Sankhya 20 (1958), 249–286. · Zbl 0228.65003
[21] Tippet, L. W.: Random sampling numbers. Tracts for computers, Nr. 15, 1927.
[22] Wold, H.: Random normal deviates. Tracts for computers, 25 (1948).
[23] Chavchanidze, V. V.: The method of random trials (Monte Carlo method). Trudy in-ta Fiziki Akad. Nauk. Gruz. SSR 3 (1955), 105.
[24] Dillard, G. M., andR. E. Simmons: An electronic generator of random numbers. Transactions of the IRE EC-11, 2 (1962).
[25] Golenko, D. J., u.V. P. Smirjagin: Eine Quelle im Intervall [0, 1] gleichverteilter Zufallszahlen. Publ. math. Inst. ung. Akad. d. Wiss. 5 (1960), 241–253.
[26] Hammersley, J. M.: Electronic computers and the analysis of stochastic processes. Math. Tab. Aids. Comput. 4 (1950), 56–57.
[27] Havel, J.: An electronic generator of random sequences. Trans. 2nd Prague Conf. Information Theory, New York 1961, 219–225.
[28] Hirai, H., andT. Mikami: Design of random walker for Monte Carlo method. Electronic device. J. Inst. Polytech. Osaka City Univ. (A) 11 (1960), 23–38.
[29] Isada, M., andH. Ikeda: Random number generator. Ann. Inst. Stat. Math. Tokyo 8 (1956), 119–126. · Zbl 0075.28903 · doi:10.1007/BF02863577
[30] Isaksson, H.: A generator of random numbers. Teleteknik 3 (1959), 25–40.
[31] Pawlak, Z.: Flip-flop as generator of random binary digits. MTAC 10 (1956), 28–30.
[32] Sterzer, F.: Random number generator using subharmonic oscillators. Rev. Scient. Instrum. 30 (1959), 241–243. · doi:10.1063/1.1716525
[33] Sugiyama, H., andO. Miyatake: Design of random walker for Monte Carlo method. J. Inst. Polytech. Osaka City Univ. (A), 10 (1959), 35–41.
[34] Allard, J. L., A. R. Dobell andT. E. Hull: Mixed congruential random number generators for decimal machines. JACM 10 (1963), 131–141. · Zbl 0116.09707 · doi:10.1145/321160.321163
[35] Bandelow, C. – ’Zufallszahlen – ihre Herstellung und Anwendung’ – Diplomarbeit an der Univ. München, 1964.
[36] Barnett, V. D.: The behaviour of pseudo-random sequences generated on computers by the multiplicative congruential method. Math. Comput. 16 (1962), 63–69. · Zbl 0108.13701 · doi:10.1090/S0025-5718-1962-0136046-5
[37] Bofinger, E., andV. J. Bofinger: On a Periodic Property of Pseudo-Random Sequences. JACM 5 (1958), 261–265. · Zbl 0091.14503 · doi:10.1145/320932.320937
[38] Certaine, J.: On sequences of pseudo-random numbers of maximal length. JACM 5 (1958), 353–356. · Zbl 0091.14504 · doi:10.1145/320941.320949
[39] Coveyou, R. R.: Serial correlation in the generation of pseudo-random numbers. JACM 7 (1960), 72–74. · Zbl 0096.33903 · doi:10.1145/321008.321018
[40] Duparc, H. J. A., C. G. Lekkerkerker, andW. Peremans: Reduced sequences of integers and pseudo-random numbers. Math. Centrum, Amsterdam, Rapp. ZW 1953 - 002.
[41] Duparc, H. J. A., andW. Peremans: Enige methods om random-numbers te maken II. Math. Centrum Amsterdam, Rapp. ZW 1952 - 013.
[42] Edmonds, A. R.: The generation of pseudo-random numbers on electronic digital computers. Comput. J. 2 (1960), 181–185. · Zbl 0091.29702 · doi:10.1093/comjnl/2.4.181
[43] Forsythe, G. E.: Generation and testing of random digits at the National Bureau of Standards. NBS Appl. Math. Ser. 12 (1951), 34–35.
[44] Franklin, J. N.: On the equidistribution of pseudo-random numbers. Quarterly Appl. Math. 16 (1958), 183–188. · Zbl 0085.12802 · doi:10.1090/qam/93501
[45] Gajewski, H., andR. Zielinski: Notes on a certain middle-square generator. Algorytmy 2, 4 (1965), 37–39.
[46] Greenberger, M.: Notes on a new pseudo-random number generator. JACM 8 (1961), 163–167. · Zbl 0104.36005 · doi:10.1145/321062.321065
[47] Greenberger, M.: An a priori determination of serial correlation in computer generated random numbers. Math. Comput. 15 (1961), 383–389; corrigenda Math. Comput. 16 (1962), 126. · Zbl 0113.33504 · doi:10.1090/S0025-5718-1961-0144489-8
[48] Greenberger, M.: Method in randomness. Comm. ACM 8 (1965), 177–179. · Zbl 0149.12611 · doi:10.1145/363791.363827
[49] Hammer, P. C.: The mid-square method of generating digits. NBS Appl. Math. Ser. 12 (1951), 33.
[50] Hoerner, S. von: Herstellung von Zufallszahlen auf Rechenautomaten. ZAMP 8 (1957), 26–52. · Zbl 0077.11606 · doi:10.1007/BF01601153
[51] Horton, H. B.: A method for obtaining random numbers. Ann. Math. Stat. 19 (1948), 81–85. · Zbl 0031.37301 · doi:10.1214/aoms/1177730294
[52] Horton, H. B., andR. T. Smith: A direct method for producing random digits in any number system. Ann. Math. Stat. 20 (1949), 82–90. · Zbl 0041.26505 · doi:10.1214/aoms/1177730092
[53] Hull, T. E., andA. R. Dobell: Random number generators. SIAM Rev. 4 (1962), 230–254. · Zbl 0111.14701 · doi:10.1137/1004061
[54] Hull, T. E., andA. R. Dobell: Mixed congruential random number generators for binary machines. JACM 11, 1 (1964), 31–40. · Zbl 0122.14001 · doi:10.1145/321203.321208
[55] Hutchinson, D. W.: A new uniform pseudorandom number generator. Comm. ACM 9 (1966), 432–433. · Zbl 0141.14603 · doi:10.1145/365696.365712
[56] Jagerman, D. L.: The autocorrelation and joint distribution functions of the sequences {a {\(\cdot\)} j2/m}, {a(j + {\(\tau\)})2/m}. Math. Comput. 18 (1964), 211–232. · Zbl 0134.14801
[57] Jagerman, D. L.: Some theorems concerning pseudo-random numbers. Math. Comput. 19 (1965), 418–426. · Zbl 0154.04803 · doi:10.1090/S0025-5718-1965-0184405-X
[58] Jansson, B.: Autocorrelations between pseudo-random numbers. Nordisk. Tidsk. Informationsbehandling 4 (1964), 6–27. · Zbl 0134.14706
[59] Johnson, D. L.: Generating and testing of pseudo-random numbers on the IBM type 701. MTAC 10 (1956), 8–13. · Zbl 0072.35705
[60] Jones, H. L.: How many of a group of random numbers will be usable in selecting a particular sample? J. Amer. Stat. Ass. 54 (1959), 102–122. · Zbl 0089.35203 · doi:10.1080/01621459.1959.10501502
[61] Kuehn, H. G.: A 48-bit pseudo random number generator. Comm. ACM 4 (1961), 350–352. · Zbl 0097.34001 · doi:10.1145/366678.366690
[62] Lehmer, D. H. – ’Mathematical methods in large-scala computing units’ – Proc. 2nd Symp. on Large-scale Digital Calculating Machinery, (1951), 141–146.
[63] Liniger, W.: On a method byD. H. Lehmer for the generation of pseudo random numbers. Numer. Math. 3 (1961), 265–270. · Zbl 0100.33702 · doi:10.1007/BF01386027
[64] MacLaren, M. D., andG. Marsaglia: Uniform random number generators. JACM 12, 1 (1965), 83–89. · Zbl 0143.40101 · doi:10.1145/321250.321257
[65] Morrison, D. R.: Geometric progressions modulo n as random number generators. Sandia Corporation Reprint SCR-22 (1958).
[66] Moshman, J.: The generation of pseudo random numbers on a decimal calculator. JACM 1 (1954), 88–91. · doi:10.1145/320772.320775
[67] Neiman, V. I., andY. V. Paramonov: A method of generating random numbers. Probl. Peredachi Inf. 2 (1962), 117–123.
[68] Page, E. S.: Pseudo-random elements for computers. Appl. Statist. 8 (1959), 124–131. · doi:10.2307/2985548
[69] Peach, P.: Bias in pseudo-random numbers. J. Amer. Stat. Assoc. 56 (1961), 610–618. · Zbl 0111.14801 · doi:10.1080/01621459.1961.10480648
[70] Rotenberg, A.: A new pseudo-random number generator. JACM 7 (1960), 75–77. · Zbl 0096.33902 · doi:10.1145/321008.321019
[71] Sibuya, M.: A method for generating uniformly distributed points on N-dimensional spheres. Ann. Inst. Stat. Math. 14 (1962), 81–85. · Zbl 0112.11203 · doi:10.1007/BF02868626
[72] Sobol, I. M.: Pseudo random numbers for the machine ”STRELA”. Theor. Prob. Appl. III (1958), 192–197. · Zbl 0124.34703 · doi:10.1137/1103019
[73] Spenser, G.: Random numbers and their generation. Computers and Automation (1955), 10, 11, 23.
[74] Stockmal, F.: Calculations with pseudo-random numbers. JACM 11, 1 (1964), 41–52. · Zbl 0125.08002 · doi:10.1145/321203.321209
[75] Thomson, W. E.: A modified congruence method of generating pseudo-random numbers. Comp. J. 1 (1958), 83. · Zbl 0087.32705 · doi:10.1093/comjnl/1.2.83
[76] Tocher, K. D.: The application of automatic computers to sampling experiments. J. Roy. Stat. Soc.; Suppl. 1b (1954), 39–61. · Zbl 0055.36902
[77] Trausworthe, R. C.: Random numbers generated by linear recurrence modulo two. Math. Comput. 19 (1965), 201–209. · doi:10.1090/S0025-5718-1965-0184406-1
[78] Vaintshtein, G. G., andV. B. Svechinskii: The theory of random number generators. Zv. An. SSSR. Tekhn. Kibernetika 4 (1963), 202–208.
[79] Votaw, D. F., andJ. A. Rafferty: High speed sampling. MTAC 5 (1951), 1–8. · Zbl 0045.06706
[80] Walsh, J. E.: Concerning compound randomization in the binary system. Ann. Math. Stat. 20 (1949), 580–589. · Zbl 0036.09105 · doi:10.1214/aoms/1177729950
[81] Yamada, S.: On the period of pseudo-random numbers generated byLehmers congruential method. J. Oper. Res. Soc. Japan 3 (1960/61), 113–123.
[82] Zierler, N.: Linear recursive sequences. J. SIAM 7 (1959), 31–48. · Zbl 0096.33804
[83] Bartholomew, D. J.: Tests for randomness in a series of events when the alternative is a trend. J. Roy. Stat. Soc., Ser. B, 18 (1956), 234–239. · Zbl 0073.15304
[84] Bartlett, M. S.: The frequency goodness of fit test for probability chains. Proc. Camb. Philos. Soc. 47 (1951), 86–95. · Zbl 0042.14404 · doi:10.1017/S0305004100026402
[85] Barton, D. E., andF. N. David: Tests for randomness of points on a line. Biometrika 43 (1956), 104–112. · Zbl 0071.35601 · doi:10.1093/biomet/43.1-2.104
[86] Barton, D. E., andF. N. David: Multiple runs. Biometrika 44 (1957), 168–178. · Zbl 0084.14601 · doi:10.1093/biomet/44.1-2.168
[87] Barton, D. E., F. N. David, andC. L. Mallows: Non-randomness in a sequence of two alternatives I. Wilcoxon’s and allied test statistics. Biometrika 45 (1958), 166–180. · Zbl 0099.13604 · doi:10.1093/biomet/45.3-4.572
[88] Barton, D. E., andF. N. David: Non-randomness in a sequence of two alternatives II. Runs test. Biometrika 45 (1958), 253–256. · Zbl 0099.13605 · doi:10.1093/biomet/45.3-4.572
[89] Bateman, G.: On the power function of the longest run as a test for randomness in a sequence of alternatives. Biometrika 35 (1948), 97–112. · Zbl 0030.20302 · doi:10.1093/biomet/35.1-2.97
[90] Billingsley, P.: Asymptotic distributions of two goodness of fit criteria. Ann. Math. Stat. 27 (1956), 1123–1129. · Zbl 0073.35605 · doi:10.1214/aoms/1177728078
[91] Bofinger, E., andV. J. Bofinger: The Gap test for random sequences. Ann. Math. Stat. 32 (1961), 524–534. · Zbl 0109.37302 · doi:10.1214/aoms/1177705058
[92] Butcher, J. C.: A partition test for pseudo-random numbers. MTAC 15 (1961), 198–199. · Zbl 0111.14702
[93] Cochran, W. G.: The {\(\chi\)}2-test of goodness of fit. Ann. Math. Stat. 23 (1952), 315–345. · Zbl 0047.13105 · doi:10.1214/aoms/1177729380
[94] David, F. N.: A power function for tests of randomness in a sequence of alternatives. Biometrika 34 (1947), 335–339. · Zbl 0029.40503 · doi:10.1093/biomet/34.3-4.335
[95] Dodd, E. L.: Certain tests for randomness applied to data grouped into small sets. Econometrica 10 (1942), 249–257. · Zbl 0063.01126 · doi:10.2307/1905467
[96] Fisser, H.: Some tests applied to pseudo-random numbers generated byv. Hoerner’s rule. Numer. Math. 3 (1961), 247–249. · Zbl 0101.10601 · doi:10.1007/BF01386024
[97] Good, I. J.: The serial test for sampling numbers and other tests for randomness. Proc. Camb. Philos. Soc. 49 (1953), 276–284. · Zbl 0051.36203 · doi:10.1017/S030500410002836X
[98] Good, I. J.: On the serial test for random sequences. Ann. Math. Stat. 28 (1957), 262–264. · Zbl 0083.14801 · doi:10.1214/aoms/1177707053
[99] Gorenflo, R.: Über Pseudozufallsgeneratoren und ihre statistischen Eigenschaften. Biometr. Zeitschrift 7 (1965), 90–93. · Zbl 0139.35701 · doi:10.1002/bimj.19650070204
[100] Grant, A. M.: Some properties of runs in smoothed random series. Biometrika 39 (1952), 198–204. · Zbl 0046.36901 · doi:10.1093/biomet/39.1-2.198
[101] Green, B. F., jr.,J. E. K. Smith, andL. Klem: Empirical tests of an additive random number generator. JACM 6 (1959), 527–537. · Zbl 0096.33901 · doi:10.1145/320998.321006
[102] Greenwood, R. E.: Coupon collector’s test for random digits. MTAC 9 (1955), 1–5. · Zbl 0064.13906
[103] Gruenberger, F.: Tests of random digits. MTAC 4 (1950), 244–245.
[104] Gruenberger, F., andA. M. Mark: The d2-test of random digits. MTAC 5 (1951), 109–110.
[105] Hunter, D. G. N.: Note on a test for repeating cycles in a pseudo-random number generator. Comp. J. 3 (1960). · Zbl 0087.32706
[106] Kendall, M. G., andB. Babington-Smith: Randomness and random sampling numbers. Roy. Stat. Soc. J. 101 (1938), 147–166. · doi:10.2307/2980655
[107] Kendall, M. G., andB. Babington-Smith: Second paper on random sampling numbers. Supp. to Roy. Stat. Soc. J. 6 (1939), 51–61. · doi:10.2307/2983623
[108] Kermack, W. O., andA. G. McKendrick: Tests for randomness in a series of numerical observations. Proc. Roy. Soc., Edinburgh, 57 (1936/37), Part 3, 228–240. · Zbl 0016.41301 · doi:10.1017/S0370164600013778
[109] Krishna Iyer, P. V., andA. S. P. Rao: Theory of the probability distribution of runs in a sequence of observations. J. Indian Soc. Agric. Statist. 5 (1953), 29–77.
[110] Levene, H.: On the power function of tests of randomness based on runs up and down. Ann. Math. Stat. 23 (1952), 34–56. · Zbl 0046.36402 · doi:10.1214/aoms/1177729484
[111] Mood, A. M.: The distribution theory of runs. Ann. Math. Stat. 11 (1940), 367–392. · Zbl 0024.05301 · doi:10.1214/aoms/1177731825
[112] Moore, P. G.: A sequential test for randomness. Biometrika 40 (1953), 111–115. · Zbl 0050.36105
[113] Namneck, P. –, Vergleich von Zufallszahlen-Generatoren’ – Elektr. Rechenanlagen 8 (1966).
[114] Olmstead, P. S.: Distribution of sample arrangements for runs up and down. Ann. Math. Stat. 17 (1946), 24–33. · Zbl 0063.06035 · doi:10.1214/aoms/1177731019
[115] Rosander, A. C.: The use of inversions as a test of random order. J. Amer. Stat. Assoc. 37 (1942), 352–358. · doi:10.1080/01621459.1942.10501763
[116] Savage, I. R.: On the independence of tests of randomness and other hypotheses. J. Amer. Stat. Assoc. 52 (1957), 53–57. · Zbl 0084.14603 · doi:10.1080/01621459.1957.10501368
[117] Swed, F. S., andC. Eisenhart: Tables for testing randomness of grouping in a sequence of alternatives. Ann. Math. Stat. 14 (1943), 66–87. · Zbl 0060.30504 · doi:10.1214/aoms/1177731494
[118] Taussky, O., andJ. Todd: Generation and testing of pseudo-random numbers. In: Symposium on Monte Carlo Methods, pp. 15–28. New York 1956.
[119] Young, L. C.: On randomness in ordered sequences. Ann. Math. Stat. 12 (1941), 293–300. · Zbl 0026.41504 · doi:10.1214/aoms/1177731711
[120] Yule, G. U.: A test of Tippett’s random sampling numbers. Roy. Stat. Soc. J., 101 (1938), 167–172. · doi:10.2307/2980656
[121] Bolshev, L. N.: On transformations of random variables. Theor. Prob. Appl. 4 (1959), 129 bis 141. · Zbl 0092.35202 · doi:10.1137/1104012
[122] Box, G. E. P., andM. E. Muller: A note on the generation of random normal deviates. Ann. Math. Stat. 29 (1958), 610–611. · Zbl 0085.13720 · doi:10.1214/aoms/1177706645
[123] Butcher, J. C.: Random sampling from the normal distribution. Comput. J. 3 (1960), 251–253. · Zbl 0094.13503 · doi:10.1093/comjnl/3.4.251
[124] Butler, J. W.: Machine sampling from given probability distributions. In: Symposium on Monte Carlo Methods, pp. 249–264. New York 1956.
[125] Clark, C. E., andB. W. Holz: Exponentially distributed random numbers. Baltimore 1960. · Zbl 0101.11703
[126] Dodd, E. L.: A transformation of Tippett’s random sampling numbers into numbers normally distributed. Bol. Mat. 15 (1942), 73–77. · Zbl 0060.29715
[127] Gebhardt, F.: Generating normally distributed random numbers by inverting the normal distribution function. Math. Comp. 18, 86 (1964), 302–306. · Zbl 0119.13406
[128] Golenko, D. I.: Generation of random numbers with arbitrary distribution law. Vycisl. Mat. 5 (1959), 83–92.
[129] Hicks, J. S., andR. F. Wheeling: An efficient method for generating uniformly distributed points on the surface of an n-dimensional sphere. Comm. ACM 2 (1959), 17–19. · Zbl 0086.11604 · doi:10.1145/377939.377945
[130] Jansson, B.: Generation of random bivariate normal deviates and computation of related integrals. BIT 4 (1964), 205–212. · Zbl 0163.40003 · doi:10.1007/BF01939512
[131] Jöhnk, M. D.: Erzeugung von betaverteilten und gammaverteilten Zufallszahlen. Metrika 8 (1964), 5–15. · Zbl 0117.13203 · doi:10.1007/BF02613706
[132] Kronmal, R.: Evaluation of a pseudorandom normal number generator. JACM 11 (1964), 357–363. · Zbl 0122.14002 · doi:10.1145/321229.321238
[133] MacLaren, M. D., G. Marsaglia, andT. A. Bray: A fast procedure for generating exponential random variables. Comm. ACM 7 (1964), 298–300. · Zbl 0127.09101 · doi:10.1145/364099.364330
[134] Marsaglia, G.: Random variables and computers. Trans. Third Prague Conf., New York 1964, 499–512.
[135] Marsaglia, G.: Generating discrete random variables in a computer. Comm. ACM 6 (1963). · Zbl 0112.08402
[136] Marsaglia, G.: Expressing a random variable in terms of uniform random variables. Ann. Math. Stat. 32 (1961), 894–898. · Zbl 0139.35604 · doi:10.1214/aoms/1177704983
[137] Marsaglia, G.: Generating exponential random variables. Ann. Math. Stat. 32 (1961), 899 bis 900. · Zbl 0139.35603 · doi:10.1214/aoms/1177704984
[138] Marsaglia, G., M. D. MacLaren, andT. A. Bray: A fast procedure for generating normal random numbers. Comm. ACM 7 (1964), 4–10. · Zbl 0127.09005 · doi:10.1145/363872.363883
[139] Marsaglia, G., andT. A. Bray: A convenient method generating normal variables. SIAM Rev. 9 (1964), 260–264. · Zbl 0125.08001 · doi:10.1137/1006063
[140] Muller, M. E.: An inverse method for the generation of random normal deviates on large-scale computers. MTAC 12 (1958), 167–174. · Zbl 0082.33602
[141] Muller, M. E.: A comparison of methods for generating normal deviates on digital computers. JACM 6 (1959), 376–383. · Zbl 0086.11601 · doi:10.1145/320986.320992
[142] Muller, M. E.: A note on a method for generating points uniformly on N-dimensional spheres. Comm. ACM 2 (1959), 19–20. · Zbl 0086.11605 · doi:10.1145/377939.377946
[143] Neumann, J. von: Various techniques used in connection with random digits. NBS Appl. Math. Ser. 12 (1951), 36–38.
[144] Scheuer, E. M., andD. S. Stoller: On the generation of normal random vectors. Technometrics 4 (1962), 278–281. · Zbl 0114.10801 · doi:10.1080/00401706.1962.10490011
[145] Sibuya, M.: On exponential and other random variable generators. Ann. Inst. Stat. Math. 13 (1961), 231–237. · Zbl 0124.34603 · doi:10.1007/BF02868873
[146] Sibuya, M.: Further consideration on normal random variable generator. Ann. Inst. Stat. Math. 14 (1962), 159–165. · Zbl 0124.34602 · doi:10.1007/BF02868636
[147] Akaike, H.: Monte Carlo Method applied to the solution of simultaneous linear equations. Ann. Inst. Stat. Math., Tokyo, 7 (1956), 107. · Zbl 0072.14401 · doi:10.1007/BF02951451
[148] Bakhvalov, N. S.: On the approximate evaluation of multiple integrals. Vestnik Mosk. Gos. Univ., Ser. mat., mekh., astr., fiz., 4 (1959), 3–18.
[149] Berger, M. J.;Dogett, J. – ’Reflection and transmission of gamma radiation by barriers: semianalytic Monte Carlo calculation’ – J. Res. Nat. Bur. Stand. 56, (1956), 89–98. · Zbl 0074.44301 · doi:10.6028/jres.056.013
[150] Blagoveshchenskii, J. N.: The effectiveness of the Monte Carlo method in some problems Vopr. Teorii mat. mashin 2 (1962), 191–197.
[151] Cerulus, F., andR. Hagedorn: A Monte Carlo method to calculate multiple phase space integrals. Nuovo Cimento (X) 9 (1958), Suppl. N 2, 646–677. · Zbl 0083.21603 · doi:10.1007/BF02747692
[152] Clark, C. E.: Sampling efficiency in Monte Carlo analysis. Ann. Inst. Stat. Math. 15 (1963).
[153] Clark, C. E.: Importance sampling in Monte Carlo analysis. Oper. Res. 9 (1961), 603–620. · Zbl 0117.36905 · doi:10.1287/opre.9.5.603
[154] Courant, R.;Friedrichs, K.;Lewy, H. – ’Über die partiellen Differenzengleichungen der math. Physik’ – Math. Ann. 100 (1928), 32–74. · JFM 54.0486.01 · doi:10.1007/BF01448839
[155] Curtiss, J. H.: A stochastic treatment of some classical interpolation problems. Proc. 4th Berkeley Symp. Math. Stat. Prob. 2 (1961). · Zbl 0209.20502
[156] Curtiss, J. H.: Sampling methods applied to differential and difference equations. Proc. Seminar on Scientific Computation, New York 1949.
[157] Cutkosky, R. E.: A Monte Carlo method for solving a class of integral equations. J. Res. Nat. Bur. Standards 47 (1951), 113–115. · doi:10.6028/jres.047.015
[158] Dalenius, T.: The problem of optimum stratification. Skand. Aktuarietidskr. 33 (1950), 203–213. · Zbl 0041.46302
[159] Dalenius, T., andJ. L. Hodges: The choice of stratification points. Skand. Aktuarietidskr. 3–4 (1957), 198–203.
[160] Davis, P., andP. Rabinowitz: Some Monte Carlo experiments in computing multiple integrals. MTAC 10 (1956), 1–8. · Zbl 0072.14403
[161] Donsker, M. D., andM. Kac: A sampling method for determining the lowest eigenvalue and principal eigenfunction of Schrödinger’s equation. J. Res. Nat. Bur. Stand. 44 (1950), 551–557. · doi:10.6028/jres.044.050
[162] Edmundson, H. P.: Monte Carlo matrix inversion and recurrent events. MTAC 7 (1953), 18–21. · Zbl 0050.13001
[163] Ermakov, S. M., andV. G. Zolotukhin: Polynomial approximations and the Monte Carlo Method. Theor. Prob. Appl. 5 (1960). · Zbl 0147.17601
[164] Evans, D. H.: Applied multiplex sampling. Technometrics 5 (1963), 341–359. · Zbl 0114.35301 · doi:10.1080/00401706.1963.10490103
[165] Evans, D. H.: Multiplex sampling. Ann. Math. Stat. 34 (1963). · Zbl 0119.35601
[166] Fieller, E. C., andH. O. Hartley: Sampling with control variables. Biometrika 41 (1954), 494–501. · Zbl 0056.37401 · doi:10.1093/biomet/41.3-4.494
[167] Forsythe, G. E., andR. A. Leibler: Matrix inversion by a Monte Carlo Method. MTAC 4 (1950), 127–129.
[168] Frolov, A. S., andN. N. Chentsov: The evaluation of specific integrals, which depend on a parameter, by the Monte Carlo Method. Zh. Vycisl. Mat. Mat. Fiziki 2, (1962), 714–717.
[169] Gosh, S. P.: Optimum stratification with two characters. Ann. Math. Stat. 34 (1963). · Zbl 0119.40104
[170] Gurin, L. S., andV. P. Lobach: Combination of the methods of Monte Carlo and steepest descent for solving certain extremal problems. Zh. Vycisl. Mat. Mat. Fiziki 2 (1962), 499–502.
[171] Hall, A. – ’On an experimental determination of {\(\pi\)}’ – Messeng. Math. 2 (1873), 113–114.
[172] Halton, J. H.: Sequential Monte Carlo. Proc. Camb. Phil. Soc. 58 (1962), 57–78. · Zbl 0119.14904 · doi:10.1017/S0305004100036227
[173] Halton, J. H.: On the relative merits of correlated and importance sampling for Monte Carlo integration. Proc. Camb. Phil. Soc. 61 (1965), 497–498. · Zbl 0125.08603 · doi:10.1017/S0305004100004059
[174] Halton, J. H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Num. Math. 2 (1960), 84–90. · Zbl 0090.34505 · doi:10.1007/BF01386213
[175] Halton, J. H., andD. C. Handscomb: A method for increasing the efficiency of Monte Carlo integration. JACM 4 (1957), 329–340. · doi:10.1145/320881.320889
[176] Hammersley, J. M.: Conditional Monte Carlo. JACM 3 (1956).
[177] Hammersley, J. M.: Monte Carlo methods for solving multivariable problems. Proc. N.Y. Acad. Sci. 1960. · Zbl 0111.12405
[178] Hammersley, J. M., andJ. G. Mauldon: General principles of antithetic variates. Proc. Camb. Phil. Soc. 52 (1956), 476–481. · Zbl 0071.35501 · doi:10.1017/S0305004100031467
[179] Hammersley, J. M., andK. W. Morton: Poor man’s Monte Carlo. Supp. to Roy. Stat. Soc. J. 16 (1954), 23–38. · Zbl 0055.36901
[180] Hammersley, J. M., andK. W. Morton: A new Monte Carlo technique: antithetic variates. Proc. Camb. Phil. Soc. 52 (1956), 449–475. · Zbl 0071.35404 · doi:10.1017/S0305004100031455
[181] Handscomb, D. C.: Proof of the antithetic variates theorem for n 2. Proc. Camb. Phil. Soc. 54 (1958), 300–301. · Zbl 0081.13901 · doi:10.1017/S0305004100033454
[182] Handscomb, D. C.: Remarks on a Monte-Carlo integration method. Num. Math. 6, (1964), 261–268. · Zbl 0239.65032 · doi:10.1007/BF01386074
[183] Kahan, B. C.: A practical demonstration of a needle experiment designed to give a number of concurrent estimates of {\(\pi\)}. J. R. Stat. Soc. 124 (1961), 227–239.
[184] Kahn, H.: Use of different Monte Carlo Sampling techniques. P-766 Rand Corp. (1955).
[185] Kahn, H.: Multiple quadrature by Monte Carlo methods. Mathematical methods for digital computers. New York 1960, 249–257.
[186] Kertiss, D.: Monte Carlo methods for the iteration of linear operators. Usp. mat. nauk. 12, 1 (1957), 149–174.
[187] Morton, K. W.: A generalization of the antithetic variate technique for evaluating integrals. J. Math. Phys. 36 (1957), 289–293. · Zbl 0091.14505 · doi:10.1002/sapm1957361289
[188] Moshman, J.: The application of sequential estimation to computer simulation and Monte Carlo procedures. JACM 5 (1958). · Zbl 0086.11603
[189] Muller, M. E.: Some continuous Monte Carlo methods for the Dirichlet problem. Ann. Math. Stat. 27 (1956), 569–589. · Zbl 0075.28902 · doi:10.1214/aoms/1177728169
[190] Opler, A.: Monte Carlo matrix calculation with punched card machines. MTAC 5 (1951), 115–120. · Zbl 0044.33203
[191] Page, E. S.: The Monte Carlo solution of some integral equations. Proc. Camb. Phil. Soc. 50 (1954), 414–425. · Zbl 0055.35805 · doi:10.1017/S0305004100029522
[192] Simon, H. A., andT. A. van Wormer: Some Monte-Carlo estimates of the Yule-distribution. Behav. Sci. 8, 3 (1963), 203–210. · doi:10.1002/bs.3830080305
[193] Sobol, I. M.: Multidimensional integrals and the Monte Carlo method. Dokl. Akad. Nauk. SSSR (NS) 114 (1957), 706–709. · Zbl 0091.14601
[194] Sobol, I. M.: Evaluation of infinite-dimensional integrals. Zh. Vycisl. Mat. Mat. Fiziki 1 (1961), 917–922.
[195] Sobol, I. M.: The use of the{\(\omega\)} 2-distribution in estimating the error when evaluating integrals by the Monte Carlo Method. Zh. Vycisl. Mat. Mat. Fiziki 2, 4 (1962), 717–723.
[196] Todd, J.: Experiments on the inversion of a 16 {\(\times\)} 16 matrix.... NBS Appl. Math. Ser. 29 (1953), 113–115. · Zbl 0052.35001
[197] Trotter, H. F., andJ. W. Tukey: Conditional Monte Carlo for normal samples. In: Symposium on Monte Carlo methods, New York 1956, 64–79.
[198] Tsuda, T., andH. Matsumoto: A note on linear extrapolation of multivariable functions by the Monte Carlo method. JACM 13 (1966), 143–150. · Zbl 0229.65028 · doi:10.1145/321312.321324
[199] Tsuda, T., andT. Kiyono: Application of the Monte Carlo method to Systems of nonlinear algebraic equations. Num. Math. 6 (1964), 59–67. · Zbl 0131.14001 · doi:10.1007/BF01386055
[200] Tukey, J. W.: Antithesis or regression? Proc. Camb. Phil. Soc. 53 (1957), 923–924. · Zbl 0079.35701 · doi:10.1017/S0305004100033053
[201] Wasow, W.: A note on the inversion of matrices by random walks. Math. Tab. Aids Comput. 6 (1952), 78–80. · Zbl 0048.11303 · doi:10.2307/2002546
[202] Wasow, W.: Random walks and the eigenvalues of elliptic differential equations. J. Res. Nat. Bur. Stand. 46 (1951), 65–73. · doi:10.6028/jres.046.010
[203] Gruenberger, F.: Further statistics on the digits of e. MTAC 6 (1952), 123–134.
[204] Kelley, D. H., andJ. N. Buxton: MONTECODE – an interpretive program for Monte Carlo simulations. Comp. J. 5 (1962), 88–93. · Zbl 0108.13803 · doi:10.1093/comjnl/5.2.88
[205] Lord Kelvin – ’Nineteenth century clouds over the dynamical theory of heat and light’ – Phil. Mag. (6) 2 (1901), 1–40. · JFM 32.0819.02 · doi:10.1080/14786440109462664
[206] Lejeune-Dirichlet. P. T. – ’Vorlesungen zur Zahlentheorie’ – herausgegeben von R. Dedekind, V. Suppl., Braunschweig 1863.
[207] Metropolis, N. C., G. Reitwiesner, andJ. von Neumann: Statistical treatment of values of first 2000 decimal digits of e and of{\(\pi\)} calculated on the ENIAC. MTAC 4 (1950), 109–111.
[208] Palasti, I., andA. Renyi: Monte Carlo methods as minimax strategies. Magyar. Tud. Akad. Mat. Kutato Inst. Közl 1 (1956), 529–545.
[209] Pathria, R. K.: A statistical study of randomness among the first 10000 digits of{\(\pi\)}. Math. Comput. 16 (1962), 188–197. · Zbl 0106.13402
[210] Pathria, R. K.: A statistical analysis of the first 2500 decimal places of e and 1/e. Proc. Nat. Inst. Sci. India A 27 (1961), 270–282. · Zbl 0112.11202
[211] Lord Rayleigh – ’OnJames Bernoulli’s theorem in probabilities’ – Philos. Mag.47 (1899), 246–251. · JFM 30.0213.03 · doi:10.1080/14786449908621254
[212] Royo, J., andS. Ferrer: The Spanish National Lottery as a source of random numbers. Trab. Estadist. 5 (1954), 247–256. · Zbl 0058.12605 · doi:10.1007/BF03028546
[213] Tocher, K. D.: The art of simulation. London 1963.
[214] Tompkins, C. B.: Description of a random number generating icosahedral dice produced by the Japanese Standards Association. Math. Comput. 15 (1961), 94–95. · doi:10.2307/2003109
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