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Random samples with known sample statistics: With application to variance reduction

Published: 12 December 1983 Publication History

Abstract

A number of sampling schemes are described which aim to improve the accuracy of estimators in simulation experiments. The schemes negatively correlate key sample statistics in pairs of runs or blocks of runs. Use is made of generators which produce random samples from certain distributions when sample statistics like the mean and dispersion are prescribed. Special cases considered include normal, inverse Gaussian and gamma generators. These can be used in their own right or as the basis of generators of other distributions. Guide lines are given which indicate the conditions under which the schemes might be effective.

References

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Aitchison, J (1963), Inverse distributions and independent gamma distributed products of random variables, Biometrika, Vol. 50, pp. 505-508.
[2]
Cheng, RCH (1981), The use of antithetic control variates in computer simulations. WSC Proceedings-81, Vol I, Eds Ören TI, Delfosse CM and Shub CM. IEEE, New York, pp 313-318.
[3]
Cheng, RCH (1983a), Generation of inverse Gaussian variates with given sample mean and dispersion, MATH Report 83-1, Dept. of Mathematics, UWIST, Cardiff, Britain.
[4]
Cheng, RCH (1983b), Generation of bivariate normal samples with given sample mean and covariance matrix, MATH Report, 83-2, Dept. of Mathematics, UWIST, Cardiff, Britain.
[5]
Johnson NL and Kotz (1970), Continuous univariate distributions −1, Houghton-Miffin, Boston.
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Michael JR, Schucany WR and Haas RW (1976), Generating random variates using transformations with multiple roots. The Amer. Stat. Vol.30, pp. 88-90.
[7]
Pullin, DI (1979), Generation of normal variates with given sample mean and variance, J. Stat. Comput. and Simul. Vol. 9, pp. 303-309.
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Pyke R (1956), Spacings (with Discussion), J.Roy. Statist. Soc. B, Vol. 27, pp. 395-449.
[9]
Tweedie MCK (1957), Statistical properties of inverse Gaussian distributions. I, Ann. Math. Statist., Vol. 28, pp. 362-377.

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cover image ACM Conferences
WSC '83: Proceedings of the 15th conference on Winter Simulation - Volume 2
December 1983
703 pages

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IEEE Press

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Published: 12 December 1983

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  • (1994)Designing simulation experiments for evaluating manufacturing systemsProceedings of the 26th conference on Winter simulation10.5555/193201.193978(69-76)Online publication date: 11-Dec-1994
  • (1993)Design of simulation experiments with manufacturing applicationsProceedings of the 25th conference on Winter simulation10.1145/256563.256588(69-75)Online publication date: 1-Dec-1993
  • (1986)Variance reduction methodsProceedings of the 18th conference on Winter simulation10.1145/318242.318261(60-68)Online publication date: 1-Dec-1986
  • (1985)A decomposition approach to variance reductionProceedings of the 17th conference on Winter simulation10.1145/21850.253059(23-32)Online publication date: 15-Dec-1985

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