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xpatagon
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Joined: June 1st, 2011, 1:31 pm

Cholesky matrix and triangular distribution

July 10th, 2014, 3:05 pm

Does it make sense to use a cholesky decomposition when some of the random variables are based on triangular distributions and not a normal distribution?I have a monte carlo simulation where some of the variables would probably be better modelled as triangular, but others by definition are normal, and they are all highly correlated. The underlying MC framework I have is based on Cholesky decompositions, and so any solution would have to be on this base. Is there a relatively simple way to handle this?Thanks
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Cholesky matrix and triangular distribution

July 10th, 2014, 11:44 pm

At the risk of stirring memories that some people may prefer to leave sleeping, this probably calls for a Gaussian copula. Use your Cholesky matrix to generate a set of correlated normals, and then transform the ones that needs transforming into triangulars. That is mechanically simple and would seem to satisfy your basic requirements. Whether it makes sense is more of an empirical question.