Abstract
Let X be a random variable (rv) obeying a cumulative distribution function (cdf).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
McGrath, E.J., Irving, D.C. (1975). Techniques for Efficient Monte Carlo Simulation (Vol. II, ORNL-RSIC-38).
Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods, SIAM.
Sobol, I. M. (1967). The distribution of points in a cube and the approximate evaluation of integrals. USSR Computational Mathematics and Mathematical Physics, 7(4), 86–112.
Matsumoto, M., & Nishimura, T. (1998). Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation, 8(1), 3–30.
Rubinstein, R. Y. (1981). Simulation and the Monte Carlo method. NY: Wiley.
Kalos, M. H., & Whitlock, P. A. (2008). Monte Carlo methods. NY: Wiley.
Fang, K. T., Hickernell, F. J., & Niederreiter, H. (2002). Monte Carlo and Quasi-Monte Carlo methods 2000. Berlin: Springer.
Niederreiter, H., & Spanier, J. (1998). Monte Carlo and Quasi-Monte Carlo methods. Berlin: Springer.
Liu, J. S. (2001). Monte Carlo strategies in scientific computing., Springer Series in Statistics Berlin: Springer.
L’Ecuyer, P. (1994). Uniform random number generation. Annals of Operational Research, 53, 77–120.
L’Ecuyer, P. (2011). Uniform random number generators. In: M. Lovric (Ed.), International Encyclopedia of Statistical Science Part 21(pp. 1625–1630). Berlin: Springer.
Shortle, J. F., & L’Ecuyer, P. (2011). Introduction to rare-event simulation. In Wiley Encyclopedia of Operations Research and Management Science. New York: Wiley.
L’Ecuyer, P. (2011). Random number generators. In S. I. Gass & M. C. Fu (Eds.), Wiley encyclopedia of operations research and management science (3rd ed.). Berlin: Springer.
L’Ecuyer, P., Mandjes, M., Turn, B. (2009). Importance sampling and rare event simulation. In G. Rubino, B. Turn (eds.), Rare event simulation using Monte Carlo methods (pp. 17–38). New York: Wiley.
L’Ecuyer, P., (2010). Pseudorandom number generators. In R. Cont, (Ed.), Wiley encyclopedia of quantitative finance (pp. 1431–1437). New York: Wiley.
L’Ecuyer, P. (2004). Random number generation and Quasi-Monte Carlo. In J. Teugels, B. Sundt (Eds.), Wiley encyclopedia of actuarial science (Vol. 3, pp. 1363–1369). New York: Wiley.
Marsaglia G., Bray, T.A. (1964). A convenient method for generating normal variables. SIAM Review, 6(3).
Booth, T. E. (1989). Zero-variance solutions for linear Monte Carlo. Nuclear Science and Engineering, 102, 332–340.
Hall, M. C. G. (1982). Cross-section adjustment with Monte Carlo sensitivities. Application to the Winfrith Iron Benchmark, Nuclear Science and Engineering, 81, 423–431.
Rief, H. (1984). Generalized Monte Carlo Perturbation algorithms for correlated sampling and a second-order series approach. Annals of Nuclear Energy, 11, 455–476.
Rief, H. (1987). Monte Carlo uncertainly analysis. In Y. Ronen (Ed.), CRC handbook on uncertainty analysis. Boca Raton: CRC press.
Rief, H. (1996). Stochastic perturbation analysis applied to neutral particle transfer. Advances in Nuclear Science and Technology, 23, 69–97.
Lux, I., & Koblinger, L. (1991). Monte Carlo particle transport methods: Neutron and photon calculations. Boca Raton: CRC Press.
Amster, H. J., & Djamehri, M. J. (1976). Prediction of statistical error in Monte Carlo transport calculations. Nuclear Science and Engineering, 60, 131–142.
Booth, T. E., & Amster, H. J. (1978). Prediction of Monte Carlo errors by a theory generalized to treat track-length estimators. Nuclear Science and Engineering, 65, 273–285.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Zio, E. (2013). Monte Carlo Simulation: The Method. In: The Monte Carlo Simulation Method for System Reliability and Risk Analysis. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4588-2_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4588-2_3
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4587-5
Online ISBN: 978-1-4471-4588-2
eBook Packages: EngineeringEngineering (R0)