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Random Number Generation

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Handbook of Computational Statistics

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

The fields of probability and statistics are built over the abstract concepts of probability space and random variable. This has given rise to elegant and powerful mathematical theory, but exact implementation of these concepts on conventional computers seems impossible. In practice, random variables and other random objects are simulated by deterministic algorithms. The purpose of these algorithms is to produce sequences of numbers or objects whose behavior is very hard to distinguish from that of their “truly random” counterparts, at least for the application of interest. Key requirements may differ depending on the context.For Monte Carlo methods, the main goal is to reproduce the statistical properties on which these methods are based, so that the Monte Carlo estimators behave as expected, whereas for gambling machines and cryptology, observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random.

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References

  • Aiello, W., Rajagopalan, S., Venkatesan, R.: Design of practical and provably good random number generators. J. Algorithm. 29(2), 358–389 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Asmussen, S., Glynn, P.W. Stochastic simulation, Springer, New York (2007)

    MATH  Google Scholar 

  • Blum, L., Blum, M., Schub, M.: A simple unpredictable pseudo-random number generator. SIAM J. Comput. 15(2), 364–383 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Bratley, P., Fox, B.L., Schrage, L.E.: A Guide to Simulation. (2nd edn.), Springer, New York, NY (1987)

    Book  Google Scholar 

  • Brown, M., Solomon, H.: On combining pseudorandom number generators. Ann. Stat. 1, 691–695 (1979)

    Article  MathSciNet  Google Scholar 

  • Chen, H.C., Asau, Y.: On generating random variates from an empirical distribution. AIEE Trans. 6, 163–166 (1974)

    Article  Google Scholar 

  • Cheng, R.C.H.: Random variate generation. In: Banks, J. (eds.) Handbook of Simulation, pp. 139–172. Wiley (1998); chapter 5.

    Google Scholar 

  • Collings, B.J.: Compound random number generators. J. Am. Stat. Assoc. 82(398), 525–527 (1987)

    Article  MATH  Google Scholar 

  • Conway, J.H., Sloane, N.J.A.: Sphere packings, lattices and groups. (3rd edn.) Grundlehren der Mathematischen Wissenschaften 290. Springer, New York (1999)

    Google Scholar 

  • Couture, R., L’Ecuyer, P.: On the lattice structure of certain linear congruential sequences related to AWC/SWB generators. Math. Comput. 62(206), 798–808 (1994)

    MathSciNet  Google Scholar 

  • Couture, R., L’Ecuyer, P.: Orbits and lattices for linear random number generators with composite moduli. Math. Comput. 65(213), 189–201 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Couture, R., L’Ecuyer, P.: Distribution properties of multiply-with-carry random number generators. Math. Comput. 66(218), 591–607 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Couture, R., L’Ecuyer, P.: Lattice computations for random numbers. Math. Comput. 69(230), 757–765 (2000)

    MathSciNet  MATH  Google Scholar 

  • Deng, L.-Y.: Efficient and portable multiple recursive generators of large order. ACM Trans. Model. Comput. Simulat. 15(1), 1–13 (2005)

    Article  MATH  Google Scholar 

  • Deng, L.-Y., George, E.O.: Generation of uniform variates from several nearly uniformly distributed variables. Comm. Stat. B19(1), 145–154 (1990)

    MathSciNet  Google Scholar 

  • Deng, L.-Y., Lin, D.K.J.: Random number generation for the new century. Am. Stat. 54(2), 145–150 (2000)

    MathSciNet  Google Scholar 

  • Deng, L.-Y., Xu, H.: A system of high-dimensional, efficient, long-cycle and portable uniform random number generators. ACM Trans. Model. Comput. Simulat. 13(4), 299–309 (2003)

    Article  MATH  Google Scholar 

  • Devroye, L.: Non-uniform Random Variate Generation, Springer, New York, NY (1986)

    Book  MATH  Google Scholar 

  • Devroye, L.: Nonuniform random variate generation. In: Simulation, Henderson, S.G., Nelson, B.L. (eds.) Handbooks in Operations Research and Management Science, pp. 83–121. Elsevier, Amsterdam, Netherlands (2006); Chapter 4.

    Google Scholar 

  • Eichenauer-Herrmann, J.: Pseudorandom number generation by nonlinear methods. Int. Stat. Rev. 63, 247–255 (1995)

    Article  MATH  Google Scholar 

  • Eichenauer-Herrmann, J., Herrmann, E., Wegenkittl, S.: A survey of quadratic and inversive congruential pseudorandom numbers. In: Hellekalek, P., Larcher, G., Niederreiter, H., Zinterhof, P. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in Statistics, vol. 127, pp. 66–97. Springer, New York, NY (1998)

    Google Scholar 

  • Evans, M., Swartz, T.: Approximating Integrals via Monte Carlo and Deterministic Methods, Oxford University Press, Oxford, UK (2000)

    Google Scholar 

  • Fincke, U., Pohst, M.: Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math. Comput. 44, 463–471 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  • Fishman, G.S.: Monte Carlo: Concepts, Algorithms, and applications. Springer Series in Operations Research. Springer, New York, NY (1996)

    MATH  Google Scholar 

  • Gentle, J.E.: Random Number Generation and Monte Carlo methods. (2nd edn.), Springer, New York, NY (2003)

    MATH  Google Scholar 

  • Goresky, M., Klapper, A.: Efficient multiply-with-carry random number generators with maximal period. ACM Trans. Model. Comput. Simulat. 13(4), 310–321 (2003)

    Article  MATH  Google Scholar 

  • Hellekalek, P., Wegenkittl, S.: Empirical evidence concerning AES. ACM Trans. Model. Comput. Simulat. 13(4), 322–333 (2003)

    Article  Google Scholar 

  • Hörmann, W., Leydold, J.: Dec. Automatic random variate generation for simulation input. In: Joines, J.A., Barton, R.R., Kang, K., Fishwick, P.A. (eds.) In: Proceedings of the 2000 Winter Simulation Conference, pp. 675–682. IEEE Press, Pistacaway, NJ (2000)

    Google Scholar 

  • Hörmann, W., Leydold, J.: Continuous random variate generation by fast numerical inversion. ACM Trans. Model. Comput. Simulat. 13(4), 347–362 (2003)

    Article  Google Scholar 

  • Hörmann, W., Leydold, J., Derflinger, G.: Automatic Nonuniform Random Variate Generation. Springer, Berlin (2004)

    MATH  Google Scholar 

  • Kinderman, A.J., Monahan, J.F.: Computer generation of random variables using the ratio of uniform deviates. ACM Trans. Math. Software 3, 257–260 (1977)

    Article  MATH  Google Scholar 

  • Knuth, D.E.: The art of Computer Programming, Seminumerical Algorithms, vol. 2, (3rd edn.) Addison-Wesley, Reading, MA (1998)

    Google Scholar 

  • Kronmal, R.A., Peterson, A.V.: An Acceptance-complement Analogue of the Mixture-plus-acceptance-rejection Method for Generating Random Variables. ACM Trans. Math. Software 10, 271–281 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  • Lagarias, J.C.: Pseudorandom numbers. Stat. Sci. 8(1), 31–39 (1993)

    Article  MathSciNet  Google Scholar 

  • Law, A.M., Kelton, W.D.: Simulation Modeling and Analysis. (3rd edn.), McGraw-Hill, New York, NY (2000)

    Google Scholar 

  • L’Ecuyer, P.: Random numbers for simulation. Comm. ACM 33(10), 85–97 (1990)

    Article  Google Scholar 

  • L’Ecuyer, P.: Uniform random number generation. Ann. Oper. Res. 53, 77–120 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P.: Combined multiple recursive random number generators. Oper. Res. 44(5), 816–822 (1996a)

    Article  MATH  Google Scholar 

  • L’Ecuyer, P.: Maximally equidistributed combined Tausworthe generators. Math. Comput. 65(213), 203–213 (1996b)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P.: Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS J. Comput. 9(1), 57–60 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P.: Random number generation. In: Banks, J. (eds.) Handbook of Simulation, pp. 93–137. Wiley (1998); chapter 4.

    Google Scholar 

  • L’Ecuyer, P.: Good parameters and implementations for combined multiple recursive random number generators. Oper. Res. 47(1), 159–164 (1999a)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P.: Tables of linear congruential generators of different sizes and good lattice structure. Math. Comput. 68(225), 249–260 (1999b)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P.: Tables of maximally equidistributed combined LFSR generators. Math. Comput. 68(225), 261–269 (1999c)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P.: Software for uniform random number generation: Distinguishing the good and the bad. In: Proceedings of the 2001 Winter Simulation Conference, pp. 95–105. IEEE Press, Pistacaway, NJ (2001)

    Google Scholar 

  • L’Ecuyer, P.: Polynomial integration lattices. In: Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2002, pp. 73–98. Springer, Berlin (2004)

    Chapter  Google Scholar 

  • L’Ecuyer, P.: SSJ: A Java library for stochastic simulation. Software user’s guide, available at http://www.iro.umontreal.ca/~lecuyer (2008)

  • L’Ecuyer, P.: Quasi-Monte Carlo methods with applications in finance. Finance Stochast. 13(3), 307–349 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Andres, T.H.: A random number generator based on the combination of four LCGs. Math. Comput. Simul. 44, 99–107 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Blouin, F., Couture, R.: A search for good multiple recursive random number generators. ACM Trans. Model. Comput. Simulat. 3(2), 87–98 (1993)

    Article  MATH  Google Scholar 

  • L’Ecuyer, P., Côté, S.: Implementing a random number package with splitting facilities. ACM Trans. Math. Software 17(1), 98–111 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Couture, R.: An implementation of the lattice and spectral tests for multiple recursive linear random number generators. INFORMS J. Comput. 9(2), 206–217 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Granger-Piché, J.: Combined generators with components from different families. Math. Comput. Simul. 62, 395–404 (2003)

    Article  MATH  Google Scholar 

  • L’Ecuyer, P., Hellekalek, P.: Random number generators: Selection criteria and testing. In: Hellekalek, P., Larcher, G. (eds.) Random and Quasi-Random Point Sets, Lecture Notes in Statistics, vol. 138, pp. 223–265. Springer New York, NY (1998)

    Chapter  Google Scholar 

  • L’Ecuyer, P., Lemieux, C.: Variance reduction via lattice rules. Manag. Sci. 46(9), 1214–1235 (2000)

    Article  MATH  Google Scholar 

  • L’Ecuyer, P., Lemieux, C.: Recent advances in randomized quasi-Monte Carlo methods. In: Dror, M., L’Ecuyer, P., Szidarovszky, F. (eds.) Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, pp. 419–474. Kluwer Academic, Boston (2002)

    Google Scholar 

  • L’Ecuyer, P., Mandjes, M., Tuffin, B.: Importance sampling and rare event simulation. In: Rubino, G., Tuffin, B. (eds.) Rare Event Simulation Using Monte Carlo Methods, 17–38. Wiley (2009); Chapter 2.

    Google Scholar 

  • L’Ecuyer, P., Panneton, F.: Construction of equidistributed generators based on linear recurrences modulo 2. In: Fang, K.-T., Hickernell, F.J., Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 318–330. Springer, Berlin (2002)

    Chapter  Google Scholar 

  • L’Ecuyer, P., Panneton, F.: F 2-linear random number generators. In: Alexopoulos, C., Goldsman, D.J.R. (eds.) Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman, Wilson, pp. 169–193. Springer, New York (2009)

    Google Scholar 

  • L’Ecuyer, P., Proulx, R.: Dec. About polynomial-time “unpredictable” generators. In: Proceedings of the 1989 Winter Simulation Conference, pp. 467–476: IEEE Press, New York (1989)

    Google Scholar 

  • L’Ecuyer, P., Simard, R.: Beware of linear congruential generators with multipliers of the form a =  ± 2q ± 2r. ACM Trans. Math. Software 25(3), 367–374 (1999)

    Article  MATH  Google Scholar 

  • L’Ecuyer, P., Simard, R.: On the performance of birthday spacings tests for certain families of random number generators. Math. Comput. Simul. 55(1–3), 131–137 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Simard, R.: TestU01: A C library for empirical testing of random number generators. ACM Trans. Math. Software 33(4), Article 22 (2007)

    Google Scholar 

  • L’Ecuyer, P., Simard, R., Chen, E.J., Kelton, W.D.: An object-oriented random-number package with many long streams and substreams. Oper. Res. 50(6), 1073–1075 (2002)

    Article  Google Scholar 

  • L’Ecuyer, P., Simard, R., Wegenkittl, S.: Sparse serial tests of uniformity for random number generators. SIAM J. Sci. Comput. 24(2), 652–668 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Tezuka, S.: Structural properties for two classes of combined random number generators. Math. Comput. 57(196), 735–746 (1991)

    MathSciNet  MATH  Google Scholar 

  • L’Ecuyer, P., Touzin, R.: Fast combined multiple recursive generators with multipliers of the form a =  ± 2q ± 2r. In: Joines, J.A., Barton, R.R., Kang, K., Fishwick, P.A. (eds.) Proceedings of the 2000 Winter Simulation Conference, pp. 683–689. IEEE Press, Pistacaway, NJ (2000)

    Google Scholar 

  • L’Ecuyer, P., Touzin, R.: On the Deng-Lin random number generators and related methods. Stat. Comput. 14, 5–9 (2004)

    Article  MathSciNet  Google Scholar 

  • Leeb, H.: Random numbers for computer simulation. Master’s thesis, University of Salzburg (1995)

    Google Scholar 

  • Lemieux, C., L’Ecuyer, P.: Randomized polynomial lattice rules for multivariate integration and simulation. SIAM J. Sci. Comput. 24(5), 1768–1789 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Leydold, J.: Automatic sampling with the ratio-of-uniform method. ACM Trans. Math. Software 26(1), 78–98 (2000)

    Article  MATH  Google Scholar 

  • Leydold, J.: UNU.RAN—universal non-uniform random number generators. Available at http://statmath.wu.ac.at/unuran/ (2009)

  • Luby, M.: Pseudorandomness and cryptographic applications. Princeton: Princeton University Press (1996)

    MATH  Google Scholar 

  • Lüscher, M.: A portable high-quality random number generator for lattice field theory simulations. Comput. Phys. Comm. 79, 100–110 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Marsaglia, G.: A current view of random number generators. In Computer Science and Statistics, Sixteenth Symposium on the Interface, pp. 3–10. Elsevier Science Publishers, North-Holland, Amsterdam (1985)

    Google Scholar 

  • Marsaglia, G.: The Marsaglia random number CDROM including the DIEHARD battery of tests of randomness. See http://stat.fsu.edu/pub/diehard (1996)

  • Marsaglia, G., Zaman, A.: A new class of random number generators. Ann. Appl. Probab. 1, 462–480 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Marsaglia, G., Zaman, A., Marsaglia, J.C.W.: Rapid evaluation of the inverse normal distribution function. Stat. Probab. Lett. 19, 259–266 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Matsumoto, M., Kurita, Y.: Twisted GFSR generators. ACM Trans. Model. Comput. Simul. 2(3), 179–194 (1992)

    Article  MATH  Google Scholar 

  • Matsumoto, M., Kurita, Y.: Twisted GFSR generators II. ACM Trans. Model. Comput. Simul. 4(3), 254–266 (1994)

    Article  MATH  Google Scholar 

  • Matsumoto, M., Kurita, Y.: Strong deviations from randomness in m-sequences based on trinomials. ACM Trans. Model. Comput. Simul. 6(2), 99–106 (1996)

    Article  MATH  Google Scholar 

  • Matsumoto, M., Nishimura, T.: Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  • Nelsen, R.B.: An introduction to copulas, Lecture Notes in Statistics. vol. 139, Springer, New York, NY (1999)

    Google Scholar 

  • Nelson, B.L., Yamnitsky, M.: Input modeling tools for complex problems. In: Proceedings of the 1998 Winter Simulation Conference, pp. 105–112. IEEE Press, Piscataway, NJ (1998)

    Google Scholar 

  • Niederreiter, H.: Random number generation and quasi-Monte Carlo methods, SIAM CBMS-NSF Regional Conference Series in Applied Mathematics. vol. 63 SIAM, Philadelphia, PA (1992)

    Google Scholar 

  • Niederreiter, H.: The multiple-recursive matrix method for pseudorandom number generation. Finite Fields Appl. 1, 3–30 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Niederreiter, H., Shparlinski, I.E.: Recent advances in the theory of nonlinear pseudorandom number generators. In: Fang, K.-T., Hickernell, F.J., Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 86–102. Springer, Berlin (2002)

    Chapter  Google Scholar 

  • Nishimura, T.: Tables of 64-bit Mersenne twisters. ACM Trans. Model. Comput. Simul. 10(4), 348–357 (2000)

    Article  Google Scholar 

  • Panneton, F., L’Ecuyer, P.: Random number generators based on linear recurrences in \({F}_{{2}^{w}}\). In: Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2002, pp. 367–378. Springer, Berlin (2004)

    Chapter  Google Scholar 

  • Panneton, F., L’Ecuyer, P.: On the xorshift random number generators. ACM Trans. Model. Comput. Simul. 15(4), 346–361 (2005)

    Article  Google Scholar 

  • Panneton, F., L’Ecuyer, P., Matsumoto, M.: Improved long-period generators based on linear recurrences modulo 2. ACM Trans. Math. Software 32(1), 1–16 (2006)

    Article  MathSciNet  Google Scholar 

  • Read, T.R.C., Cressie, N.A.C.: Goodness-of-fit statistics for discrete multivariate data. Springer Series in Statistics. Springer, New York, NY (1988)

    MATH  Google Scholar 

  • Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J., Vo, S.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST special publication 800-22, National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA (2001); See http://csrc.nist.gov/rng/.

  • Tausworthe, R.C.: Random numbers generated by linear recurrence modulo two. Math. Comput. 19, 201–209 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  • Tezuka, S.: Uniform random numbers: Theory and practice. Kluwer Academic Publishers, Norwell, MA (1995)

    MATH  Google Scholar 

  • Tezuka, S., L’Ecuyer, P.: Efficient and portable combined Tausworthe random number generators. ACM Trans. Model. Comput. Simul. 1(2), 99–112 (1991)

    Article  MATH  Google Scholar 

  • Tezuka, S., L’Ecuyer, P., Couture, R.: On the add-with-carry and subtract-with-borrow random number generators. ACM Trans. Model. Comput. Simul. 3(4), 315–331 (1994)

    Article  Google Scholar 

  • Tootill, J.P.R., Robinson, W.D., Eagle, D.J.: An asymptotically random Tausworthe sequence. J. ACM 20, 469–481 (1973)

    Article  MATH  Google Scholar 

  • Vattulainen, I., Ala-Nissila, T., Kankaala, K.: Physical models as tests of randomness. Phys. Rev. E 52(3), 3205–3213 (1995)

    Article  MathSciNet  Google Scholar 

  • von Neumann, J.: Various techniques used in connection with random digits. In: A.S.H. et al. (eds.) The Monte Carlo Method, vol. 12, pp. 36–38. National Bureau of Standards, Applied Mathematics Series (1951)

    Google Scholar 

  • Walker, A.J.: An efficient method for generating discrete random variables with general distributions. ACM Trans. Math. Software 3, 253–256 (1977)

    Article  MATH  Google Scholar 

  • Wang, D., Compagner, A.: On the use of reducible polynomials as random number generators. Math. Comput. 60, 363–374 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  • Wegenkittl, S., Matsumoto, M.: Getting rid of correlations among pseudorandom numbers: Discarding versus tempering. ACM Trans. Model. Comput. Simul. 9(3), 282–294 (1999)

    Article  Google Scholar 

  • Wu, P.-C.: Multiplicative, congruential random number generators with multiplier \(\pm {2}^{{k}_{1}} \pm{2}^{{k}_{2}}\) and modulus 2p − 1. ACM Trans. Math. Software 23(2), 255–265 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and a Canada Research Chair to the author. Wolfgang Hörmann, Josef Leydold, François Panneton, and Richard Simard made helpful comments and corrections on an earlier draft. The author has been asked to write chapters on Random Number Generation for several handbooks and encyclopedia over the years. Inevitably, there is a large amount of duplication between these chapters.

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  1. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, Québec, Canada

    Pierre L’Ecuyer

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  1. Pierre L’Ecuyer
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Correspondence to Pierre L’Ecuyer .

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  1. Dept. Computational & Data, Sciences, George Mason University, University Drive 4400, Fairfax, 22030-4444, Virginia, USA

    James E. Gentle

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. Dept. Socioinformation, Okayama University, Ridai-cho 1-1, Okayama, 700-0005, Japan

    Yuichi Mori

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L’Ecuyer, P. (2012). Random Number Generation. In: Gentle, J., Härdle, W., Mori, Y. (eds) Handbook of Computational Statistics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21551-3_3

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