ARVAG - Automatic nonuniform Random VAriate Generation
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Selected Literature and Publications of Our Group

Selected Literature

Uniform random numbers

The pLab site provides a survey on literature on uniform random numbers.

Automatic Methods

Wolfgang Hörmann, Josef Leydold, and Gerhard Derflinger:
 Automatic Nonuniform Random Variate Generation.
Springer-Verlag, Berlin, 2004.

(Other) Surveys on non-uniform random variate generation

The "bible" for theory of non-uniform random variate generation is

Luc Devroye: Non-Uniform Random Variate Generation. Springer-Verlag, New York, 1986.
Other surveys and introductions from different points of view are
Donald E. Knuth: The Art of Computer Programming, volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, 3rd edition, 1997.
It describes important aspects of both uniform random numbers and important aspects of non-uniform random variate generation.
John Dagpunar: Principles of Random Variate Generation. Clarendon Oxford Science Publications, 1988.
István Deák: Random number generators and simulation. Mathematical Methods of Operations Research, Akadémiai Kiadó, Budapest 1990.
James E. Gentle: Random Number Generation and Monte Carlo Methods. Statistics and Computing, Springer, New York 1998.
George S. Fishman: Monte Carlo. Concepts, algorithms, and applications. Springer series in Operations Research, New York 1996.
The following book describes some method for multivariate distributions
Mark E. Johnson: Multivariate Statistical Simulation. Wiley Series in Probability and Mathematical Statistics, Applied Probability and Statistics, John Wiley & Sons, New York 1987.

Publications of Our Group

Books   |   Journals   |   Conference Proceedings   |   Preprints

Books:
  1. W. Hörmann, J. Leydold, and G. Derflinger
    Automatic Nonuniform Random Variate Generation
    Springer-Verlag, Berlin Heidelberg (2004)

Journals:
  1. W. Hörmann and J. Leydold
    Continuous Random Variate Generation by Fast Numerical Inversion
    ACM Trans. Model. Comput. Simul. 13(4), pp. 347-362 (2003)

  2. J. Leydold, G. Derflinger, G. Tirler, and W. Hörmann
    An Automatic Code Generator for Nonuniform Random Variate Generation
    Mathematics and Computers in Simulation 62(3-6), pp. 405-412 (2003)

  3. J. Leydold
    Short universal generators via generalize ratio-of-uniforms method
    Math. Comput. 72, pp. 1453-1471 (2003)

  4. W. Hörmann
    A Note on the Performance of the "Ahrens Algorithm"
    Computing 69(1), pp. 83-89 (2002)

  5. W. Hörmann and G. Derflinger
    Fast Generation of Order Statistics
    ACM Transactions on Modeling and Computer Simulation 12(2), pp. 83-93 (2002)

  6. J. Leydold
    A Simple Universal Generator for Continuous and Discrete Univariate T-concave Distributions
    ACM Transactions on Mathematical Software 27(1), pp. 66-82 (2001)

  7. J. Leydold
    A Note on Transformed Density Rejection
    Computing 65(2), pp. 187-192 (2000)

  8. J. Leydold
    Automatic Sampling with the Ratio-of-uniforms Method
    ACM Transactions on Mathematical Software 26(1), pp. 78-98 (2000)

  9. W. Hörmann
    Algorithm 802: An Automatic Generator for Bivariate Log-Concave Distributions
    ACM Transactions on Mathematical Software 26(1), 201-219 (2000)

  10. J. Leydold
    A Rejection Technique for Sampling from Log-Concave Multivariate Distributions
    ACM Transactions on Modeling and Computer Simulation 8(3), pp. 254-280 (1998)

  11. J. Leydold and W. Hörmann
    A Sweep-Plane Algorithm for Generating random tuples in simple polytopes
    Mathematics of Computation 67, pp. 1617-1635 (1998)

  12. W. Hörmann and G. Derflinger
    Rejection-inversion to generate variates from monotone discrete distributions
    ACM Transactions on Modelling and Computer Simulation, 6(3), 169-184 (1996)

  13. W. Hörmann
    A rejection technique for sampling from T-concave distributions
    ACM Transactions on Mathematical Software 21(2), 182-193 (1995)

  14. W. Hörmann
    A universal generator for discrete log-concave distributions
    Computing 52, 89-96 (1994)

  15. W. Hörmann
    A note on the quality of random variates generated by the ratio of uniforms method
    ACM Transactions on Modelling and Computer Simulation 4(1), 96-106 (1994)

  16. W. Hörmann and G. Derflinger
    The transformed rejection method for generating random variables, an alternative to the ratio of uniforms method
    Communications in Statistics: Simulation and Computation 23(3), 847-860 (1994)

  17. W. Hörmann and G. Derflinger
    A portable uniform random number generator well suited for the rejection method
    ACM Transactions on Mathematical Software 19(4), 489-495 (1993)

  18. W. Hörmann
    The generation of binomial random variates
    Journal of Statistical Computation and Simulation 46, 101-110 (1993)

  19. W. Hörmann
    The transformed rejection method for generating Poisson random variables
    Insurance: Mathematics and Economics 12, 39-45 (1993)

  20. W. Hörmann and G. Derflinger
    The ACR method for generating normal random variables
    OR Spektrum 12, 181-185 (1990)

Conference Proceedings:
  1. G. Tirler and J. Leydold
    Automatic Nonuniform Random Variate Generation in R
    in: K. Hornik and F. Leisch (eds.), Proc. of the 3rd International Workshop on Distributed Statistical Computing (DSC2003) (2003)

  2. J. Leydold, E. Janka, and W. Hörmann
    Variants of Transformed Density Rejection and Correlation Induction
    in: K.-T. Fang,F.J. Hickernell, and H. Niederreiter (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 345-356 (2002)

  3. J. Leydold and W. Hörmann
    Universal Algorithms as an Alternative for Generating Non-Uniform Continuous Random Variates
    in: G.I. Schuëler, P.D. Spanos (eds.), Monte Carlo Simulation, pp. 177-183 (2001)

  4. W. Hörmann and J. Leydold
    Automatic Random Variate Generation for Simulation Input
    in: J. A. Joines, R. Barton, P. Fishwick, K. Kang (eds.), Proceedings of the 2000 Winter Simulation Conference, pp. 675-682 (2000)

  5. W. Hörmann and O. Bayar
    Modelling Probability Distributions from Data and its Influence on Simulation
    In: I. Troch and F. Breitenecker (eds.), Proceedings IMACS Symposium on Mathematical Modeling, Argesim Report No. 15, pp. 429-435 (2000)

  6. J. Leydold, H. Leeb and W. Hörmann
    Higher-Dimensional Properties of Non-Uniform Pseudo-Random Variates
    in: H. Niederreiter, J. Spanier (eds.), Monte Carlo and Quasi-Monte Carlo Methods 1998, pp. 341-355 (2000)

  7. J. Leydold and W. Hörmann
    Black Box Algorithms for Generating Non-Uniform Continuous Random Variates
    in: W. Jansen and J. G. Bethlehem (eds.), COMPSTAT 2000, Short Communications and Posters, pp. 53-54 (2000)

  8. W. Hörmann and G. Derflinger
    An automatic generator for a large class of unimodal discrete distributions
    in: A.R. Kaylan and A. Lehmann, ESM 97, pp. 139-144, SCS (1997)

  9. J. Leydold and W. Hörmann
    The automatic generation of one- and multi-dimensional distributions with transformed density rejection
    in: A. Sydow (ed.), Proc. 15th IMACS world congress, Vol. 2, pp. 757-760 (1997)

  10. M. A. Hauser, W. Hörmann, R. M. Kunst and J. Lenneis
    A note on generation, estimation and prediction of stationary processes
    in: R. Dutter and W. Grossmann, Compstat, Proceedings in Computational Statistics, pp. 323-328, Physica-Verlag, Heidelberg (1994)

  11. W. Hörmann and G. Derflinger
    Universal generators for correlation induction
    in: R. Dutter and W. Grossmann, Compstat, Proceedings in Computational Statistics, pp. 52-57, Physica-Verlag, Heidelberg (1994)

  12. W. Hörmann
    The quality of non-uniform random numbers
    in: H. Dyckhoff et al., Operations Research Proceedings 1993, pp. 329-335 Springer-Verlag, Berlin (1994)

  13. W. Hörmann
    New generators of normal and Poisson deviates based on the transformed rejection method
    in: K.-W. Hansmann et al., Operations Research Proceedings 1992, pp. 334-341, Springer-Verlag, Berlin (1993)

  14. L. Afflerbach and W. Hörmann
    Nonuniform random numbers: a sensitivity analysis for transformation methods
    in: U. Dieter and G.Ch. Pflug, International Workshop on Computationally Intensive Methods in Simulation and Optimization, Lecture Notes in Econom. Math. Systems 374, Springer-Verlag (1992)

Preprints:
  1. J. Leydold and W. Hörmann
    Smoothed Transformed Density Rejection
    submitted to Monte Carlo Methods and Applications

  2. W. Hörmann and J. Leydold
    Improved Perfect Slice Sampling
    submitted to Statistics and Computing

  3. G. Tirler, P. Dalgaard, W. Hörmann, and J. Leydold
    An Error in the Kinderman-Ramage Method and How to Fix It
    submitted to Computational Statistics & Data Analysis

  4. M. A. Hauser and W. Hörmann
    The generation of stationary Gaussian time series
    Technical Report, Institut für Statistik, Wirtschaftsuniversität Wien (1994)

Literature
  
[ARVAG]     Wolfgang Hörmann and Josef Leydold   (October 21st, 2003) Research supported by FWF