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Generation of correlated random numbers

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Generation of correlated random numbers from univariate distributions

Igor Hlivka

MUFJ Securities International, LONDON



This application is an extension of an earlier document on multivariate distributions and demonstrates how Maple can be used to generate random samples from such distribution. In a narrow sense, it presents the tool for generation of correlated samples. The sampling need for multi-factor random variables (RV) with a given correlation structure arises in many applications in economics, finance, but also in natural sciences such as genetics, physics etc. and here we show that such task can be accomplished with ease using Maple’s Statistics and Linear Algebra packages.


The multivariate RV are typically generated from univariate samples and translated into correlated ones with matrix transformation techniques. Here we will be presenting the two most common techniques:


 LU Decomposition


 SV Decomposition


The presented cases are generic - i.e. not restricted in dimensionality space so the user can create multivariate samples of the required size and dimension.


Generation of univariate samples


Correlated RV through LU Decomposition


Correlated RV through SV Decomposition


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