TY - GEN

T1 - Applications of TPNT in Multivariate Monte Carlo Simulation

AU - Chen, Xingyuan

AU - Tung, Yeou-Koung

PY - 2003/12/1

Y1 - 2003/12/1

N2 - In engineering design and analysis, proper assessment of stochastic features of model outputs is essential to account for the existence of various uncertainties. Monte Carlo simulation provides a viable tool to reproduce the stochastic features of the model outputs by generating statistically plausible realizations for random model inputs and parameters. Although there are a variety of generators developed for problems involving univariate random variable or independent random variables, generating multivariate random variates is more restricted to a few distributions whose joint probability density functions (PDFs) are known. Since most engineering problems involve multiple correlated random variables whose joint PDF is normally very difficult to establish, practical algorithms are needed to generate correlated random variables with a mixture of marginal distributions and correlation structure or even less information. In this paper, the third-order polynomial normal transform (TPNT) technique is applied to the Monte Carlo simulation, which enables one to generate correlated random variables with much less information than joint PDF. Using the TPNT, arbitrary univariate or multivariate random variates can be generated from univariate or multivariate normal distributions utilizing orthogonal transform and normal transform. The information needed is the marginal distributions and correlation structure, or sample data of the involved random variables. As compared with the existing model, the proposed algorithm shows comparable results with less information required.

AB - In engineering design and analysis, proper assessment of stochastic features of model outputs is essential to account for the existence of various uncertainties. Monte Carlo simulation provides a viable tool to reproduce the stochastic features of the model outputs by generating statistically plausible realizations for random model inputs and parameters. Although there are a variety of generators developed for problems involving univariate random variable or independent random variables, generating multivariate random variates is more restricted to a few distributions whose joint probability density functions (PDFs) are known. Since most engineering problems involve multiple correlated random variables whose joint PDF is normally very difficult to establish, practical algorithms are needed to generate correlated random variables with a mixture of marginal distributions and correlation structure or even less information. In this paper, the third-order polynomial normal transform (TPNT) technique is applied to the Monte Carlo simulation, which enables one to generate correlated random variables with much less information than joint PDF. Using the TPNT, arbitrary univariate or multivariate random variates can be generated from univariate or multivariate normal distributions utilizing orthogonal transform and normal transform. The information needed is the marginal distributions and correlation structure, or sample data of the involved random variables. As compared with the existing model, the proposed algorithm shows comparable results with less information required.

UR - http://www.scopus.com/inward/record.url?scp=1642558342&partnerID=8YFLogxK

U2 - 10.1061/40685(2003)219

DO - 10.1061/40685(2003)219

M3 - Conference contribution

AN - SCOPUS:1642558342

SN - 0784406855

T3 - World Water and Environmental Resources Congress

SP - 54

EP - 63

BT - World Water and Environmental Resources Congress

A2 - Bizier, P.

A2 - DeBarry, P.

Y2 - 23 June 2003 through 26 June 2003

ER -