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An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions

Author

Listed:
  • Philip M. Lurie

    (Institute for Defense Analyses, 1801 N. Beauregard Street, Alexandria, Virginia 22311-1772)

  • Matthew S. Goldberg

    (Institute for Defense Analyses, 1801 N. Beauregard Street, Alexandria, Virginia 22311-1772)

Abstract

This paper presents an algorithm for generating correlated vectors of random numbers. The user need not fully specify the joint distribution function; instead, the user "partially specifies" only the marginal distributions and the correlation matrix. The algorithm may be applied to any set of continuous, strictly increasing distribution functions; the marginal distributions need not all be of the same functional form. The correlation matrix is first checked for mathematical consistency (positive semi-definiteness), and adjusted if necessary. Then the correlated random vectors are generated using a combination of Cholesky decomposition and Gauss-Newton iteration. Applications are made to cost analysis, where correlations are often present between cost elements in a work breakdown structure.

Suggested Citation

  • Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, vol. 44(2), pages 203-218, February.
  • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:2:p:203-218
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    File URL: http://dx.doi.org/10.1287/mnsc.44.2.203
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    References listed on IDEAS

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    1. Parrish, Rudolph S., 1990. "Generating random deviates from multivariate Pearson distributions," Computational Statistics & Data Analysis, Elsevier, vol. 9(3), pages 283-295, May.
    2. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
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    Cited by:

    1. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    2. I-Tung Yang, 2006. "Using Gaussian copula to simulate repetitive projects," Construction Management and Economics, Taylor & Francis Journals, vol. 24(9), pages 901-909.
    3. Hui, Yer Van & Gao, Jia & Leung, Lawrence & Wallace, Stein, 2014. "Airfreight forwarder’s shipment planning under uncertainty: A two-stage stochastic programming approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 66(C), pages 83-102.
    4. Stanhope, Stephen, 2005. "Case studies in multivariate-to-anything transforms for partially specified random vector generation," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 68-79, August.
    5. Ilich, Nesa, 2009. "A matching algorithm for generation of statistically dependent random variables with arbitrary marginals," European Journal of Operational Research, Elsevier, vol. 192(2), pages 468-478, January.
    6. Ponomareva, K. & Roman, D. & Date, P., 2015. "An algorithm for moment-matching scenario generation with application to financial portfolio optimisation," European Journal of Operational Research, Elsevier, vol. 240(3), pages 678-687.
    7. repec:spr:eurjdp:v:5:y:2017:i:1:d:10.1007_s40070-017-0071-2 is not listed on IDEAS
    8. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    9. Fleten, Stein-Erik & Hoyland, Kjetil & Wallace, Stein W., 2002. "The performance of stochastic dynamic and fixed mix portfolio models," European Journal of Operational Research, Elsevier, vol. 140(1), pages 37-49, July.
    10. Pier Alda FERRARI & Alessandro BARBIERO, 2011. "Generating ordinal data," Departmental Working Papers 2011-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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