Package com.imsl.test.example.stat

Class RandomEx2

java.lang.Object
com.imsl.test.example.stat.RandomEx2
public class RandomEx2 extends Object

Generates a pseudorandom multivariate sequence with user defined marginal distributions.

This example uses method Random.nextGaussianCopula to generate a multivariate sequence GCdevt[k=0..nseq-1][j=0..nvar-1] whose marginal distributions are user-defined and imprinted with a user-specified correlation matrix CorrMtrxIn[i=0..nvar-1][j=0..nvar-1] and then uses method Random.canonicalCorrelation to extract from this multivariate random sequence a canonical correlation matrix CorrMtrx[i=0..nvar-1][j=0..nvar-1].

This example illustrates two useful copula related procedures. The first procedure generates a random multivariate sequence with arbitrary user-defined marginal deviates whose dependence is specified by a user-defined correlation matrix. The second procedure is the inverse of the first: an arbitrary multivariate deviate input sequence is first mapped to a corresponding sequence of empirically derived variates, i.e. cumulative distribution function values representing the probability that each random variable has a value less than or equal to the input deviate. The variates are then inverted, using the inverse Normal(0,1) function, to N(0,1) deviates; and finally, a canonical covariance matrix is extracted from the multivariate N(0,1) sequence using the standard sum of products.

This example demonstrates that the nextGaussianCopula method correctly embeds the user-defined correlation information into an arbitrary marginal distribution sequence by extracting the canonical correlation from these sequences and showing that they differ from the original correlation matrix by a small relative error, which generally decreases as the number of multivariate sequence vectors increases.

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