Monte Carlo Simulation for Correlated Variables with Marginal Distributions

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Abstract
As computation speed increases, Monte Carlo simulation is becoming a viable tool for engineering design and analysis. However, restrictions are often imposed on multivariate cases in which the involved stochastic parameters are correlated. In multivariate Monte Carlo simulation, a joint probability distribution is required that can only be derived for some limited cases. This paper proposes a practical multivariate Monte Carlo simulation that preserves the marginal distributions of random variables and their correlation structure without requiring the complete joint distribution. For illustration, the procedure is applied to the reliability analysis of a bridge pier against scouring.

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