| Summary: | 碩士 === 大葉工學院 === 工業工程研究所 === 84 === In the process of simulations,the input model often need a set
of relative random variables to respond the true condition. And
the random variables can have different probable distributions.
But most of the literatures of the generation of
multivariate simulations emphasized one of the special
multivariate family or time series. So the past literatures
weren't content with the need of general multivariables. The
thesis aimed above questions . In the conditions of having
every marginal distribution and a reasonable relative matrix,
we develope the algorithms of the multivariate generation.
We propose a new algorithm -- "generation of multivariate random
vectors using retrospective approximation methods" to
generate multivariate random vectors with specified marginal
distributions and a specified correlation matrix. Users need
only provide the inverse function of different marginal
distributions. The algorithms generate multivariate random
vectors with marginal-oriented approach. But before using
the marginal-oriented approach, $n(n-1)/2$ equations
must be solved. We use retrospective approximation
algorithms to solve these stochastic root-finding problems.
We also improve the algorithms to aries the efficiency by
solving concurrently $n(n-1)/2$ equations.
We progress the simulated experiments with the algorithms --
"generation of multivariate random vectors using
retrospective approximation methods". In the most specified
distributions, the algorithms can get good accuracy and
efficiency.We analysize the property of stochastic root-finding
equations and discuss the correlations between variables that be
generated with the algorithms that be proposed by us.In
addition to the restriction , we also ask that users can
conclude and provide a reasonable correlation matrix to make
the algorithms executing the correct "cholesky decomposition".
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