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

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...

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Bibliographic Details
Published in:Management science 1998-02, Vol.44 (2), p.203-218
Main Authors: Lurie, Philip M, Goldberg, Matthew S
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation
Correlation
Correlations
Cost allocation
Cost analysis
Cost estimates
Distribution
Exact sciences and technology
Gauss-Newton Method
Hessian matrices
Integral equations
Jacobians
Mathematics
Matrices
Multivariate analysis
Operational research and scientific management
Operational research. Management science
Operations research
Probability and statistics
Random Number Generation
Random variables
Risk assessment
Risk theory. Actuarial science
Sampling
Sciences and techniques of general use
Simulation
Statistical methods
Statistics
Studies
Total costs
Variable costs
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Description
Summary: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.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.44.2.203