[1]

M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions. Dover, New York, 1970.

[2]

J. H. Ahrens and U. Dieter. Computer methods for sampling from gamma, beta, poisson and bionomial distributions. Computing, 12:223–246, 1972.

[3]

J. H. Ahrens and U. Dieter. Computer generation of poisson deviates from modified normal distributions. ACM Trans. Math. Software, 8:163–179, 1982.

[4]

J. H. Ahrens and U. Dieter. Generating gamma variates by a modified rejection technique. Communications of the ACM, 25:47–54, 1982.

[5]

H. Albrecher and M. Predota. On Asian option pricing for NIG Lévy processes. Journal of computational and applied mathematics, 172:153–168, 2004.

[6]

T. W. Anderson and D. A. Darling. Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Annals of Mathematical Statistics, 23:193–212, 1952.

[7]

N. H. Anderson and D. M. Titterington. A comparison of two statistics for detecting clustering in one dimension. Journal of Statistical Computation and Simulation, 53:103–125, 1995.

[8]

I. A. Antonov and V. M. Saleev. An economic method of computing LP_τ-sequences. Zh. Vychisl. Mat. i. Mat. Fiz., 19:243–245, 1979. In Russian.

[9]

S. Asmussen and P. W. Glynn. Stochastic Simulation. Springer-Verlag, New York, 2007.

[10]

A. N. Avramidis and P. L'Ecuyer. Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance-gamma model. Management Science, 52(12):1930–1944, 2006.

[11]

A. N. Avramidis, P. L'Ecuyer, and P.-A. Tremblay. Efficient simulation of gamma and variance-gamma processes. In Proceedings of the 2003 Winter Simulation Conference, pages 319–326, Piscataway, New Jersey, 2003. IEEE Press.

[12]

A. N. Avramidis, A. Deslauriers, and P. L'Ecuyer. Modeling daily arrivals to a telephone call center. Management Science, 50(7):896–908, 2004.

[13]

A. N. Avramidis, N. Channouf, and P. L'Ecuyer. Efficient correlation matching for normal copula dependence when univariate marginals are discrete. INFORMS Journal of Computing, 21:88–106, 2009.

[14]

R. W. Bailey. Polar generation of random variates with the t-distribution. Mathematics of Computation, 62(206):779–781, 1994.

[15]

O. E. Barndorff-Nielsen. Processes of normal inverse gaussian type. Finance and Stochastics, 2:41–68, 1998.

[16]

A. Berlinet and L. Devroye. A comparison of kernel density estimates. Publications de l'Institut de Statistique de l'Université de Paris, 38(3):3–59, 1994. available at http://cgm.cs.mcgill.ca/ luc/np.html.

[17]

D. J. Best and D. E. Roberts. Algorithm AS 91: The percentage points of the χ² distribution. Applied Statistics, 24:385–388, 1975.

[18]

D. J. Best. A simple algorithm for the computer generation of random samples from a Student's t or symmetric beta distribution. In L. C. A. Corsten and J. Hermans, editors, COMPSTAT 1978: Proceedings in Computational statistics, pages 341–347, Vienna, 1978. Physica-Verlag.

[19]

G. P. Bhattacharjee. The incomplete gamma integral. Applied Statistics, 19:285–287, 1970. AS32.

[20]

Z. W. Birnbaum and S. C. Saunders. A new family of life distributions. Journal of Applied Probability, 6:319–327, 1969.

[21]

J. M. Blair, C. A. Edwards, and J. H. Johnson. Rational Chebyshev approximations for the inverse of the error function. Mathematics of Computation, 30:827–830, 1976.

[22]

L. N. Bol'shev. Some applications of Pearson transformations. Review of the Internat. Stat. Institute, 32:14–16, 1964.

[23]

G. E. P. Box and M. E. Muller. A note on the generation of random normal deviates. Annals of Mathematical Statistics, 29:610–611, 1958.

[24]

P. Bratley and B. L. Fox. Algorithm 659: Implementing Sobol's quasirandom sequence generator. ACM Transactions on Mathematical Software, 14(1):88–100, 1988.

[25]

P. Bratley, B. L. Fox, and L. E. Schrage. A Guide to Simulation. Springer-Verlag, New York, NY, second edition, 1987.

[26]

P. Bratley, B. L. Fox, and H. Niederreiter. Implementation and tests of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation, 2:195–213, 1992.

[27]

J. R. Brown and M. E. Harvey. Rational arithmetic Mathematica functions to evaluate the one-sided one-sample K-S cumulative sample distribution. Journal of Statistical Software, 19(6):1–32, 2007.

[28]

J. R. Brown and M. E. Harvey. Rational arithmetic Mathematica functions to evaluate the two-sided one sample K-S cumulative sample distribution. Journal of Statistical Software, 26(2):1–40, 2008.

[29]

E. Buist and P. L'Ecuyer. A Java library for simulating contact centers. In M. E. Kuhl, N. M. Steiger, F. B. Armstrong, and J. A. Joines, editors, Proceedings of the 2005 Winter Simulation Conference, pages 556–565. IEEE Press, 2005.

[30]

E. Buist and P. L'Ecuyer. ContactCenters: A Java Library for Simulating Contact Centers,

Software user's guide, available at http://www.simul.umontreal.ca/contactcenters.

[31]

B. H. Camp. Approximation to the point binomial. Ann. Math. Stat., 22:130–131, 1951.

[32]

R. Cao, A. Cuevas, and W. González-Manteiga. A comparative study of several smoothing methods for density estimation. Computational Statistics and Data Analysis, 17:153–176, 1994.

[33]

R. C. H. Cheng. The generation of gamma variables with non-integral shape parameter. Applied Statistics, 26:71–75, 1977.

[34]

R. C. H. Cheng. Generating beta variates with nonintegral shape parameters. Communications of the ACM, 21:317–322, 1978.

[35]

C. W. Clenshaw. Chebychev series for mathematical functions. National Physical Laboratory Mathematical Tables 5, Her Majesty's Stationery Office, London, 1962.

[36]

J. C. Cox, J. E. Ingersoll, and S. A. Ross. A theory of the term structure of interest rates. Econometrica, 53:385–407, 1985.

[37]

R. Cranley and T. N. L. Patterson. Randomization of number theoretic methods for multiple integration. SIAM Journal on Numerical Analysis, 13(6):904–914, 1976.

[38]

S. Csörg H o and J. J. Faraway. The exact and asymptotic distributions of Cramér-von mises statistics. Journal of the Royal Statistical Society, Series B, 58:221–234, 1996.

[39]

A. M. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland, and W. B. Jones. Handbook of Continued Fractions for Special Functions. Springer Netherlands, 2008.

[40]

D. A. Darling. On the theorems of Kolmogorov-Smirnov. Theory of Probability and Its Applications, V(4):356–360, 1960.

[41]

D. A. Darling. On the asymptotic distribution of Watson's statistic. The Annals of Statistics, 11(4):1263–1266, 1983.

[42]

C. de Boor. A Practical Guide to Splines. Number 27 in Applied Mathematical Sciences Series. Springer-Verlag, New York, 1978.

[43]

G. Derflinger, W. Hörmann, and J. Leydold. Random variate generation by numerical inversion when only the density is known. Preprint of the Department of Statistics and Mathematics 78, Wirtschaftsuniversität Wien, Austria, 2008. See http://epub.wu-wien.ac.at/english/.

[44]

G. Derflinger, W. Hörmann, and J. Leydold. Random variate generation by numerical inversion when only the density is known. ACM Transactions on Modeling and Computer Simulation, 20(4):Article 18, 2010.

[45]

L. Devroye and L. Györfi. Nonparametric Density Estimation: The L₁ View. John Wiley, New York, NY, 1985.

[46]

L. Devroye. Non-Uniform Random Variate Generation. Springer-Verlag, New York, NY, 1986.

[47]

L. Devroye. Random variate generation in one line of code. In Proceedings of the 1996 Winter Simulation Conference, pages 265–271. IEEE Press, 1996.

[48]

L. Devroye. Nonuniform random variate generation. In S. G. Henderson and B. L. Nelson, editors, Simulation, Handbooks in Operations Research and Management Science, pages 83–121. Elsevier, Amsterdam, The Netherlands, 2006. Chapter 4.

[49]

J. Dick and F. Pillichshammer. Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press, Cambridge, U.K., 2010.

[50]

J. Dick. Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Manuscript, Sydney, Australia, 2008.

[51]

J. Dick. On quasi-Monte Carlo rules achieving higher order convergence. In P. L'Ecuyer and A. B. Owen, editors, Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 73–96, Berlin, 2009. Springer-Verlag.

[52]

A. R. DiDonato and A. H. Morris. Significant digit computation of the incomplete beta function ratios. ACM Transactions on Mathematical Software, 18(3):360–377, 1992.

[53]

T. G. Donnelly. Algorithm 462: Bivariate normal distribution. Communications of the ACM, 16(10):638, 1973.

[54]

Z. Drezner and G. O. Wesolowsky. On the computation of the bivariate normal integral. Journal of Statistical Computation and Simulation, 35:101–107, 1990.

[55]

J. Durbin. Distribution Theory for Tests Based on the Sample Distribution Function. SIAM CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA, 1973.

[56]

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

[57]

M. Evans, N. Hastings, and B. Peacock. Statistical Distributions. Wiley, 3rd edition, 2000.

[58]

H. Faure and C. Lemieux. Generalized Halton sequences in 2008: A comparative study. ACM Transactions on Modeling and Computer Simulation, 19(4):Article 15, 2009.

[59]

H. Faure and S. Tezuka. Another random scrambling of digital (t,s)-sequences. In K.-T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000, pages 242–256, Berlin, 2002. Springer-Verlag.

[60]

H. Faure. Good permutations for extreme discrepancy. Journal of Number Theory, 42:47–56, 1992.

[61]

W. Feller. An Introduction to Probability Theory and Its Applications, Vol. 2. Wiley, New York, NY, first edition, 1966.

[62]

G. S. Fishman. Discrete Event Simulation: Modeling, Programming, and Analysis. Springer Series in Operations Research. Springer-Verlag, New York, NY, 2001.

[63]

M. R. Flynn. Fitting human exposure data with the Johnson S_B distribution. Journal of Exposure Science and Environmental Epidemiology, 16:56–62, 2006.

[64]

B. L. Fox. Implementation and relative efficiency of quasirandom sequence generators. ACM Transactions on Mathematical Software, 12:362–376, 1986.

[65]

E. Gamma, R. Helm, R. Johnson, and J. Vlissides. Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley, Reading, MA, second edition, 1998.

[66]

J. E. Gentle. Random Number Generation and Monte Carlo Methods. Springer, New York, NY, 1998.

[67]

A. Genz. Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Statistics and Computing, 14:151–160, 2004. See http://www.math.wsu.edu/faculty/genz/homepage.

[68]

I. B. Gertsbakh and Y. Shpungin. Models of Network Reliability. CRC Press, Boca Raton, FL, 2010.

[69]

P. Glasserman. Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004.

[70]

J. Glaz, J. Naus, and S. Wallenstein. Scan statistics. Springer Series in Statistics. Springer, New York, NY, 2001.

[71]

J. Glaz. Approximations and bounds for the distribution of the scan statistic. Journal of the American Statistical Association, 84:560–566, 1989.

[72]

P. W. Glynn and R. Szechtman. Some new perspectives on the method of control variates. In K.-T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000, pages 27–49, Berlin, 2002. Springer-Verlag.

[73]

R. B. Goldstein. Algorithm 451: Chi-square quantiles. Communications of the ACM, 16:483–485, 1973.

[74]

J. Gosling, B. Joy, and G. L. Steele Jr. The Java Language Specification. Addison-Wesley, second edition, 2000. Also available from http://java.sun.com/docs/books/jls.

[75]

A. W. Grace and I. A. Wood. Approximating the tail of the Anderson–Darling distribution. Computational Statistics and Data Analysis, 56(12):4301–4311, 2012.

[76]

J. H. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik, 2:84–90, 1960.

[77]

C. H. Hamilton and A. Rau-Chaplin. Compact Hilbert indices for multidimensional data. In Proceedings of the First International Conference on Complex, Intelligent, and Software Intensive Systems (CISIS'07), pages 139–146. IEEE, 2007.

[78]

J. M. Hammersley. Monte Carlo methods for solving multivariate problems. Annals of the New York Academy of Science, 86:844–874, 1960.

[79]

P. Hellekalek and H. Niederreiter. The weighted spectral test: Diaphony. ACM Transactions on Modeling and Computer Simulation, 8(1):43–60, 1998.

[80]

F. J. Hickernell, H. S. Hong, P. L'Ecuyer, and C. Lemieux. Extensible lattice sequences for quasi-Monte Carlo quadrature. SIAM Journal on Scientific Computing, 22(3):1117–1138, 2001.

[81]

F. J. Hickernell. A generalized discrepancy and quadrature error bound. Mathematics of Computation, 67(221):299–322, 1998.

[82]

F. J. Hickernell. Lattice rules: How well do they measure up? In P. Hellekalek and G. Larcher, editors, Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics, pages 109–166. Springer-Verlag, New York, 1998.

[83]

F. J. Hickernell. Goodness-of-fit statistics, discrepancies and robust designs. Statistics and Probability Letters, 44:73–78, 1999.

[84]

F. J. Hickernell. Obtaining O(N^-2+ε) convergence for lattice quadrature rules. In K.-T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000, pages 274–289, Berlin, 2002. Springer-Verlag.

[85]

N. J. Higham. The scaling and squaring method for the matrix exponential revisited. SIAM Review, 51(4):747–764, 2009.

[86]

G. W. Hill. Algorithm 395: Student's t-distribution. Communications of the ACM, 13:617–619, 1970.

[87]

W. Höermann and G. Derflinger. The ACR method for generating normal random variables. OR Spektrum, 12:181–185, 1990.

[88]

H. S. Hong and F. H. Hickernell. Algorithm 823: Implementing scrambled digital sequences. ACM Transactions on Mathematical Software, 29:95–109, 2003.

[89]

W. Hörmann and J. Leydold. Automatic random variate generation for simulation input. In J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, editors, Proceedings of the 2000 Winter Simulation Conference, pages 675–682, Piscataway, NJ, Dec 2000. IEEE Press.

[90]

W. Hörmann, J. Leydold, and G. Derflinger. Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin, 2004.

[91]

Wolfgang Hoschek. The Colt Distribution: Open Source Libraries for High Performance Scientific and Technical Computing in Java. CERN, Geneva, 2004. Available at http://acs.lbl.gov/software/colt/.

[92]

J. S. Huang and P. S. Shen. More maximum likelihood oddities. Journal of Statistical Planning and Inference, 137(7):2151–2155, 2007.

[93]

R. Ibrahim, P. L'Ecuyer, N. Régnard, and H. Shen. On the modeling and forecasting of call center arrivals. In C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher, editors, Proceedings of the 2012 Winter Simulation Conference, pages 256–267. IEEE Press, 2012.

[94]

R. Ibrahim, H. Ye, P. L'Ecuyer, and H. Shen. Modeling and forecasting call center arrivals: A literature study and a case study. International Journal of Forecasting, 32(3):865–874, 2016.

[95]

J. Imai and K. S. Tan. A general dimension reduction technique for derivative pricing. Journal of Computational Finance, 10(2):129–155, 2006.

[96]

J. J. Moré and B. S. Garbow and K. E. Hillstrom. User Guide for MINPACK-1, Report ANL-80-74. Argonne, Illinois, USA, 1980. See http://www-fp.mcs.anl.gov/otc/Guide/softwareGuide/Blurbs/minpack.html.

[97]

N. L. Johnson and S. Kotz. Distributions in Statistics: Discrete Distributions. Houghton Mifflin, Boston, 1969.

[98]

N. L. Johnson and S. Kotz. Distributions in Statistics: Continuous Multivariate Distributions. John Wiley, New York, NY, 1972.

[99]

N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions, volume 1. Wiley, 2nd edition, 1994.

[100]

N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions, volume 2. Wiley, 2nd edition, 1995.

[101]

N. L. Johnson. Systems of frequency curves generated by methods of translation. Biometrika, 36:149–176, 1949.

[102]

V. Kachitvichyanukul and B. Schmeiser. Computer generation of hypergeometric random variates. J. Statist. Comput. Simul., 22:127–145, 1985.

[103]

A. Kalemanova, B. Schmid, and R. Werner. The normal inverse gaussian distribution for synthetic CDO pricing. Journal of derivatives, 14(3):80–93, 2007.

[104]

A. W. Kemp. Efficient generation of logarithmically distributed pseudo-random variables. Applied Statistics, 30:249–253, 1981.

[105]

W. J. Kennedy Jr. and J. E. Gentle. Statistical Computing. Dekker, New York, NY, 1980.

[106]

A. J. Kinderman and J. G. Ramage. Computer generation of normal random variables. Journal of the American Statistical Association, 71:893–898, 1976.

[107]

J. H. Kingston. Analysis of tree algorithms for the simulation event lists. Acta Informatica, 22:15–33, 1985.

[108]

J. H. Kingston. Analysis of Henriksen's algorithm for the simulation event set. SIAM Journal on Computing, 15:887–902, 1986.

[109]

L. Kleinrock. Queueing Systems, Vol. 1. Wiley, New York, NY, 1975.

[110]

M. Knott. The distribution of the Cramér-von Mises statistic for small sample sizes. Journal of the Royal Statistical Society B, 36:430–438, 1974.

[111]

D. E. Knuth. The Art of Computer Programming, Vol. 1. Addison-Wesley, Reading, MA, second edition, 1973.

[112]

D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, third edition, 1998.

[113]

N. M. Korobov. The approximate computation of multiple integrals. Dokl. Akad. Nauk SSSR, 124:1207–1210, 1959. in Russian.

[114]

S. Kotz and J. R. van Dorp. BEYOND BETA, Other Continuous Families of Distributions with Bounded Support and Applications. World Scientific Publishing co., Singapore, 2004.

[115]

K. Krishnamoorthy. Handbook of statistical distributions with applications. Chapman & Hall/CRC Press, Boca Raton, FL, 2006.

[116]

G. Latouche and V. Ramaswami. Introduction to matrix analytic methods in stochastic modeling. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999.

[117]

S. S. Lavenberg and P. D. Welch. A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations. Management Science, 27:322–335, 1981.

[118]

A. M. Law and W. D. Kelton. Simulation Modeling and Analysis. McGraw-Hill, New York, NY, third edition, 2000.

[119]

A. M. Law. Simulation Modeling and Analysis. McGraw-Hill, New York, fifth edition, 2014.

[120]

P. L'Ecuyer and T. H. Andres. A random number generator based on the combination of four LCGs. Mathematics and Computers in Simulation, 44:99–107, 1997.

[121]

P. L'Ecuyer and E. Buist. Simulation in Java with SSJ. In M. E. Kuhl, N. M. Steiger, F. B. Armstrong, and J. A. Joines, editors, Proceedings of the 2005 Winter Simulation Conference, pages 611–620, Piscataway, NJ, 2005. IEEE Press.

[122]

P. L'Ecuyer and S. Côté. Implementing a random number package with splitting facilities. ACM Transactions on Mathematical Software, 17(1):98–111, 1991.

[123]

P. L'Ecuyer and J. Granger-Piché. Combined generators with components from different families. Mathematics and Computers in Simulation, 62:395–404, 2003.

[124]

P. L'Ecuyer and C. Lemieux. Quasi-Monte Carlo via linear shift-register sequences. In Proceedings of the 1999 Winter Simulation Conference, pages 632–639. IEEE Press, 1999.

[125]

P. L'Ecuyer and C. Lemieux. Variance reduction via lattice rules. Management Science, 46(9):1214–1235, 2000.

[126]

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

[127]

P. L'Ecuyer and D. Munger. Constructing adapted lattice rules using problem-dependent criteria. In Proceedings of the 2012 Winter Simulation Conference, pages 373–384. IEEE Press, 2012.

[128]

P. L'Ecuyer and D. Munger. On figures of merit for randomly-shifted lattice rules. In H. Wozniakowski and L. Plaskota, editors, Monte Carlo and Quasi-Monte Carlo Methods 2010, pages 133–159, Berlin, 2012. Springer-Verlag.

[129]

P. L'Ecuyer and D. Munger. Algorithm 958: Lattice builder: A general software tool for constructing rank-1 lattice rules. ACM Trans. on Mathematical Software, 42(2):Article 15, 2016.

[130]

P. L'Ecuyer and A. B. Owen, editors. Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer-Verlag, Berlin, 2010.

[131]

P. L'Ecuyer and F. Panneton. Construction of equidistributed generators based on linear recurrences modulo

In K.-T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000, pages 318–330. Springer-Verlag, Berlin, 2002.

[132]

P. L'Ecuyer and G. Perron. On the convergence rates of IPA and FDC derivative estimators. Operations Research, 42(4):643–656, 1994.

[133]

P. L'Ecuyer and R. Simard. TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators, 2002. Software user's guide. Available at http://www.iro.umontreal.ca/ lecuyer.

[134]

P. L'Ecuyer and R. Simard. Inverting the symmetrical beta distribution. ACM Transactions on Mathematical Software, 32(4):509–520, 2006.

[135]

P. L'Ecuyer and R. Touzin. Fast combined multiple recursive generators with multipliers of the form a = ± 2^q ± 2^r. In J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, editors, Proceedings of the 2000 Winter Simulation Conference, pages 683–689, Piscataway, NJ, 2000. IEEE Press.

[136]

P. L'Ecuyer, L. Meliani, and J. Vaucher. SSJ: A framework for stochastic simulation in Java. In E. Yücesan, C.-H. Chen, J. L. Snowdon, and J. M. Charnes, editors, Proceedings of the 2002 Winter Simulation Conference, pages 234–242. IEEE Press, 2002.

[137]

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

[138]

P. L'Ecuyer, R. Simard, and S. Wegenkittl. Sparse serial tests of uniformity for random number generators. SIAM Journal on Scientific Computing, 24(2):652–668, 2002.

[139]

P. L'Ecuyer, C. Lécot, and B. Tuffin. A randomized quasi-Monte Carlo simulation method for Markov chains. Operations Research, 56(4):958–975, 2008.

[140]

P. L'Ecuyer, J. S. Parent-Chartier, and M. Dion. Simulation of a Lévy process by PCA sampling to reduce the effective dimention. In Proceedings of the 2008 Winter Simulation Conference, pages 436–443, Piscataway, NJ, 2008. IEEE Press.

[141]

P. L'Ecuyer, C. Lécot, and A. L'Archevêque-Gaudet. On array-RQMC for Markov chains: Mapping alternatives and convergence rates. In P. L'Ecuyer and A. B. Owen, editors, Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 485–500, Berlin, 2009. Springer-Verlag.

[142]

P. L'Ecuyer, D. Munger, and N. Kemerchou. clRNG: A random number API with multiple streams for OpenCL. report, http://www.iro.umontreal.ca/ lecuyer/myftp/papers/clrng-api.pdf, 2015.

[143]

P. L'Ecuyer, D. Munger, C. Lécot, and B. Tuffin. Sorting methods and convergence rates for Array-RQMC: Some empirical comparisons. Mathematics and Computers in Simulation, 143:191–201, 2016. http://dx.doi.org/10.1016/j.matcom.2016.07.010.

[144]

P. L'Ecuyer, D. Munger, B. Oreshkin, and R. Simard. Random numbers for parallel computers: Requirements and methods, with emphasis on GPUs. Mathematics and Computers in Simulation, 135:3–17, 2017. Open access at http://dx.doi.org/10.1016/j.matcom.2016.05.005.

[145]

P. L'Ecuyer. Random numbers for simulation. Communications of the ACM, 33(10):85–97, 1990.

[146]

P. L'Ecuyer. Uniform random number generation. Annals of Operations Research, 53:77–120, 1994.

[147]

P. L'Ecuyer. Maximally equidistributed combined Tausworthe generators. Mathematics of Computation, 65(213):203–213, 1996.

[148]

P. L'Ecuyer. Good parameters and implementations for combined multiple recursive random number generators. Operations Research, 47(1):159–164, 1999.

[149]

P. L'Ecuyer. Tables of maximally equidistributed combined LFSR generators. Mathematics of Computation, 68(225):261–269, 1999.

[150]

P. L'Ecuyer. Software for uniform random number generation: Distinguishing the good and the bad. In Proceedings of the 2001 Winter Simulation Conference, pages 95–105, Piscataway, NJ, 2001. IEEE Press.

[151]

P. L'Ecuyer. Quasi-Monte Carlo methods for simulation. In Proceedings of the 2003 Winter Simulation Conference, pages 81–90, Piscataway, NJ, 2003. IEEE Press.

[152]

P. L'Ecuyer. Polynomial integration lattices. In H. Niederreiter, editor, Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 73–98, Berlin, 2004. Springer-Verlag.

[153]

P. L'Ecuyer. Quasi-Monte Carlo methods in finance. In Proceedings of the 2004 Winter Simulation Conference, pages 1645–1655, Piscataway, New Jersey, 2004. IEEE Press.

[154]

P. L'Ecuyer. Random number generation. In J. E. Gentle, W. Haerdle, and Y. Mori, editors, Handbook of Computational Statistics, pages 35–70. Springer-Verlag, Berlin, 2004. Chapter II.2.

[155]

P. L'Ecuyer. SSJ: A Java Library for Stochastic Simulation, 2004. Software user's guide, available at http://www.iro.umontreal.ca/ lecuyer.

[156]

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

[157]

P. L'Ecuyer. Random number generation. In J. E. Gentle, W. Haerdle, and Y. Mori, editors, Handbook of Computational Statistics, pages 35–71. Springer-Verlag, Berlin, second edition, 2012.

[158]

P. L'Ecuyer. Random number generation with multiple streams for sequential and parallel computers. In Proceedings of the 2015 Winter Simulation Conference, pages 31–44. IEEE Press, 2015.

[159]

P. L'Ecuyer. History of uniform random number generation. In Proceedings of the 2017 Winter Simulation Conference, pages 202–230. IEEE Press, 2017.

[160]

P. L'Ecuyer. Randomized quasi-Monte Carlo: An introduction for practitioners. In P. W. Glynn and A. B. Owen, editors, Monte Carlo and Quasi-Monte Carlo Methods: MCQMC 2016, pages 29–52, Berlin, 2018. Springer.

[161]

C. Lemieux and P. L'Ecuyer. Randomized polynomial lattice rules for multivariate integration and simulation. SIAM Journal on Scientific Computing, 24(5):1768–1789, 2003.

[162]

C. Lemieux, M. Cieslak, and K. Luttmer. RandQMC User's Guide: A Package for Randomized Quasi-Monte Carlo Methods in C, 2004. Software user's guide, available at http://www.math.uwaterloo.ca/ clemieux/randqmc.html.

[163]

C. Lemieux. L'utilisation de règles de réseau en simulation comme technique de réduction de la variance. PhD thesis, Université de Montréal, May 2000.

[164]

F. C. Leone, L. S. Nelson, and R. B. Nottingham. The folded normal distribution. Technometrics, 3(4):543–550, 1961.

[165]

P. A. W. Lewis. Distribution of the Anderson-Darling statistic. Annals of Mathematical Statistics, 32:1118–1124, 1961.

[166]

J. Leydold and W. Hörmann. UNU.RAN—A Library for Universal Non-Uniform Random Number Generators, 2002. Available at http://statistik.wu-wien.ac.at/unuran.

[167]

J. J. Liang, K. T. Fang, F. J. Hickernell, and R. Li. Testing multivariate uniformity and its applications. Mathematics of Computation, 70(233):337–355, 2000.

[168]

C. Liu, R. Martin, and N. Syring. Simulating from a gamma distribution with small shape parameter. ArXiv e-prints, February 2013.

[169]

D. B. Madan and F. Milne. Option pricing with V.G. martingale components. Mathematical Finance, 1:39–55, 1991.

[170]

D. B. Madan and E. Seneta. The variance gamma (V.G.) model for share market returns. Journal of Business, 63:511–524, 1990.

[171]

D. B. Madan, P. P. Carr, and E. C. Chang. The variance gamma process and option pricing. European Finance Review, 2:79–105, 1998.

[172]

K. V. Mardia and P. J. Zemroch. Tables of the F and Related Distributions with Algorithms. Academic Press, London, 1978.

[173]

G. Marsaglia and J. Marsaglia. Evaluating the Anderson-Darling distribution. Journal of Statistical Software, 9(2):1–5, 2004. See http://www.jstatsoft.org/v09/i02/.

[174]

G. Marsaglia, A. Zaman, and J. C. W. Marsaglia. Rapid evaluation of the inverse normal distribution function. Statistics and Probability Letters, 19:259–266, 1994.

[175]

G. Marsaglia, W. W. Tsang, and J. Wang. Evaluating Kolmogorov's distribution. Journal of Statistical Software, 8(18):1–4, 2003. URL is http://www.jstatsoft.org/v08/i18/.

[176]

G. Marsaglia. Improving the polar method for generating a pair of random variables. Technical report, Boeing Scientific Research Laboratory, Seattle, Washington, 1962.

[177]

G. Marsaglia. A current view of random number generators. In L. Billard, editor, Computer Science and Statistics, Sixteenth Symposium on the Interface, pages 3–10, North-Holland, Amsterdam, 1985. Elsevier Science Publishers.

[178]

J. Matousek. Geometric Discrepancy: An Illustrated Guide. Springer-Verlag, Berlin, 1999.

[179]

M. Matsumoto and T. Nishimura. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation, 8(1):3–30, 1998.

[180]

J. R. Michael, W. R. Schuchany, and R. W. Haas. Generating random variates using transformations with multiple roots. The American Statistician, 30:88–90, 1976.

[181]

W. Molenaar. Approximations to the Poisson, Binomial and Hypergeometric Distribution Functions, volume 31 of Mathematical Center Tract. Mathematisch Centrum, Amsterdam, 1970.

[182]

W. J. Morokoff and R. E. Caflisch. Quasi-random sequences and their discrepancies. SIAM Journal on Scientific Computing, 15:1251–1279, 1994.

[183]

S. L. Moshier. Cephes math library, 2000. See http://www.moshier.net.

[184]

M. F. Neuts. Matrix-Geometric Solutions in Stochastic Models. John Hopkins, University Press, Baltimore, 1981.

[185]

H. Niederreiter and C. Xing. Nets, (t,s)-sequences, and algebraic geometry. In P. Hellekalek and G. Larcher, editors, Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics, pages 267–302. Springer, New York, NY, 1998.

[186]

H. Niederreiter. Low-discrepancy point sets obtained by digital constructions over finite fields. Czechoslovak Math. Journal, 42:143–166, 1992.

[187]

H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods, volume 63 of SIAM CBMS-NSF Reg. Conf. Series in Applied Mathematics. SIAM, 1992.

[188]

Dirk Nuyens. The construction of good lattice rules and polynomial lattice rules. In Peter Kritzer, Harald Niederreiter, Friedrich Pillichshammer, and Arne Winterhof, editors, Uniform Distribution and Quasi-Monte Carlo Methods: Discrepancy, Integration and Applications, pages 223–255. De Gruyter, 2014.

[189]

E. H. Oliver. A maximum likelihood oddity. The American Statistician, 26(3):43––44, 1972.

[190]

B. Oreshkin, N. Régnard, and P. L'Ecuyer. Rate-based daily arrival process models with application to call centers. Operations Research, 64(2):510–527, 2016.

[191]

A. B. Owen. Randomly permuted (t,m,s)-nets and (t,s)-sequences. In H. Niederreiter and P. J.-S. Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics, pages 299–317. Springer-Verlag, 1995.

[192]

A. B. Owen. Monte Carlo variance of scrambled equidistribution quadrature. SIAM Journal on Numerical Analysis, 34(5):1884–1910, 1997.

[193]

A. B. Owen. Scrambled net variance for integrals of smooth functions. Annals of Statistics, 25(4):1541–1562, 1997.

[194]

A. B. Owen. Latin supercube sampling for very high-dimensional simulations. ACM Transactions on Modeling and Computer Simulation, 8(1):71–102, 1998.

[195]

A. B. Owen. Variance with alternative scramblings of digital nets. ACM Transactions on Modeling and Computer Simulation, 13(4):363–378, 2003.

[196]

F. Panneton and P. L'Ecuyer. Random number generators based on linear recurrences in F_2^w. In H. Niederreiter, editor, Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 367–378, Berlin, 2004. Springer-Verlag.

[197]

F. Panneton and P. L'Ecuyer. Infinite-dimensional point sets based on linear recurrences over GF(2^w). In H. Niederreiter and D. Talay, editors, Monte Carlo and Quasi-Monte Carlo Methods 2004, Berlin,

Springer-Verlag. to appear.

[198]

F. Panneton, P. L'Ecuyer, and M. Matsumoto. Improved long-period generators based on linear recurrences modulo 2. ACM Transactions on Mathematical Software, 32(1):1–16, 2006.

[199]

F. Panneton. Construction d'ensembles de points basée sur des récurrences linéaires dans un corps fini de caractéristique 2 pour la simulation Monte Carlo et l'intégration quasi-Monte Carlo. PhD thesis, Département d'informatique et de recherche opérationnelle, Université de Montréal, Canada, August 2004.

[200]

E. S. Pearson. Note on an approximation to the distribution of non-central χ². Biometrika, 46:364, 1959.

[201]

D. B. Peizer and J. W. Pratt. A normal approximation for binomial, F, beta, and other common related tail probabilities. Journal of the American Statistical Association, 63:1416–1456, 1968.

[202]

W. Pelz and I. J. Good. Approximating the lower tail-areas of the Kolmogorov-Smirnov one-sample statistic. Journal of the Royal Statistical Society B, 38(2):152–156, 1976.

[203]

S. Penev and T. Raykov. A Wiener germ approximation of the noncentral chi square distribution and of its quantiles. Computational Statistics, 15(2):219–228, 2000.

[204]

D. S. G. Pollock. Smoothing with cubic splines. Technical report, University of London, Queen Mary and Westfield College, London, 1993.

[205]

J. Pomeranz. Exact cumulative distribution of the Kolmogorov-Smirnov statistic for small samples (algorithm 487). Communications of the ACM, 17(12):703–704, 1974.

[206]

Vikas Chandrakant Raykar and Ramani Duraiswami. Fast optimal bandwidth selection for kernel density estimation. In Proceedings of the 2006 SIAM International Conference on Data Mining, pages 524–528, 2006.

[207]

T. R. C. Read and N. A. C. Cressie. Goodness-of-Fit Statistics for Discrete Multivariate Data. Springer Series in Statistics. Springer-Verlag, New York, NY, 1988.

[208]

C. Ribeiro and N. Webber. Valuing path-dependent options in the variance-gamma model by Monte Carlo with a gamma bridge. manuscript, December 2002.

[209]

S. M. Ross. Introduction to Probability Models. Academic Press, ninth edition, 2007.

[210]

H. Sakasegawa. Stratified rejection and squeeze method for generating beta random numbers. Annals of the Institute of Mathematical Statistics, 35B:291–302, 1983.

[211]

R. B. Schnabel. UNCMIN—Unconstrained Optimization Package, FORTRAN. University of Colorado at Boulder. See http://www.ici.ro/camo/unconstr/uncmin.htm.

[212]

J. L. Schonfelder. Chebyshev expansions for the error and related functions. Mathematics of Computation, 32:1232–1240, 1978.

[213]

David W. Scott. Multivariate Density Estimation. Wiley, 2015.

[214]

R. J. Serfling. Approximation Theorems for Mathematical Statistics. Wiley, New York, NY, 1980.

[215]

B. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 1986.

[216]

R. Simard and P. L'Ecuyer. Computing the two-sided Kolmogorov-Smirnov distribution. Journal of Statistical Software, 39(11), 2011. URL is http://www.jstatsoft.org/v39/i11.

[217]

B. Skaflestad and W. M. Wright. The scaling and modified squaring method for matrix functions related to the exponential. Applied Numerical Mathematics, 59(3-4):783–799, 2009.

[218]

D. D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. Journal of the Association for Computing Machinery, 32(3):652–686, 1985.

[219]

I. H. Sloan and S. Joe. Lattice Methods for Multiple Integration. Clarendon Press, Oxford, 1994.

[220]

I. H. Sloan and S. Joe. Lattice methods for multiple integration. Oxford Science Publications. The Clarendon Press Oxford University Press, New York, 1994.

[221]

I. M. Sobol'. The distribution of points in a cube and the approximate evaluation of integrals. U.S.S.R. Comput. Math. and Math. Phys., 7(4):86–112, 1967.

[222]

I. M. Sobol'. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. Academy of Sciences, 16:236–242, 1976.

[223]

E. Stadlober and H. Zechner. Generating beta variates via patchwork rejection. Computing, 50:1–18, 1993.

[224]

M. A. Stephens. Use of the Kolmogorov-Smirnov, Cramér-Von Mises and related statistics without extensive tables. Journal of the Royal Statistical Society, Series B, 33(1):115–122, 1970.

[225]

M. S. Stephens. Tests based on EDF statistics. In R. B. D'Agostino and M. S. Stephens, editors, Goodness-of-Fit Techniques. Marcel Dekker, New York and Basel, 1986.

[226]

M. S. Stephens. Tests for the uniform distribution. In R. B. D'Agostino and M. S. Stephens, editors, Goodness-of-Fit Techniques, pages 331–366. Marcel Dekker, New York and Basel, 1986.

[227]

J. Struckmeier. Fast generation of low-discrepancy sequences. Journal of Computational and Applied Mathematics, 61(4):29–41, 1995.

[228]

S. Tezuka and H. Faure. i-binomial scrambling of digital nets and sequences. Technical report, IBM Research, Tokyo Research Laboratory, 2002.

[229]

S. Tezuka and P. L'Ecuyer. Efficient and portable combined Tausworthe random number generators. ACM Transactions on Modeling and Computer Simulation, 1(2):99–112, 1991.

[230]

S. Tezuka. Uniform Random Numbers: Theory and Practice. Kluwer Academic, 1995.

[231]

G. Tirler, P. Dalgaard, W. Hörmann, and J. Leydold. An error in the Kinderman-Ramage method and how to fix it. Computational Statistics and Data Analysis, 47(3):433–440, 2004.

[232]

G. Ulrich. Computer generation of distributions on the m-sphere. Applied Statistics, 33:158–163, 1984.

[233]

S. P. Verrill. UNCMIN—Unconstrained Optimization Package, Java. US Forest Service, Forest Products Laboratory. Available at http://www1.fpl.fs.fed.us/optimization.html.

[234]

S. R. Wallenstein and N. Neff. An approximation for the distribution of the scan statistic. Statistics in Medicine, 6:197–207, 1987.

[235]

X. Wang and F. J. Hickernell. Randomized Halton sequences. Mathematical and Computer Modelling, 32:887–899, 2000.

[236]

T. T. Warnock. Computational investigations of low discrepancy point sets. In S. K. Zaremba, editor, Applications of Number Theory to Numerical Analysis, pages 319–343, London, 1972. Academic Press.

[237]

T. T. Warnock. Computational investigation of low-discrepancy point sets. In H. Niederreiter and P. J.-S. Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics, pages 354–361. Springer-Verlag, 1995.

[238]

G. S. Watson. Optimal invariant tests for uniformity. In Studies in Probability and Statistics, pages 121–127. North Holland, Amsterdam, 1976.

[239]

N. Webber and C. Ribeiro. A Monte Carlo method for the normal inverse gaussian option valuation model using an inverse gaussian bridge. Technical Report 5, Society for Computational Economics, 2003.

[240]

W. Whitt. Dynamic staffing in a telephone call center aiming to immediately answer all calls. Operations Research Letters, 24(5):205–212, 1999.