Hello

I have a matrix aaa like this:

           aa1       aa2       aa3
[1,]  8371.417  27613.57  1170.466
[2,] 14317.999  42421.82  3423.934
[3,] 22026.466  59874.14  8103.084
[4,] 33884.986  84506.34 19176.764
[5,] 57954.968 129824.30 56097.310

where each column represents an empirical distribution of random variates (normally the number of rows would be, say, 10,000 or 100,000) and a matrix bbb of percentiles like this:

bbb

           [,1]      [,2]      [,3]
[1,] 0.70092980 0.8144194 0.6200732
[2,] 0.77968803 0.5804948 0.5463661
[3,] 0.01509415 0.9313509 0.8611973
[4,] 0.22654757 0.6183386 0.4962867
[5,] 0.36548835 0.6608696 0.3062784
What I'd like to do is to apply the quantiles in the three columns of bbb to the columns of aaa independently, so as to obtain a matrix ccc such that, for example, ccc[3,1]=quantile(aaa[,1],bbb[3,1]). THe complete matrix is:


ccc =    quantile(aaa[,1],bbb[1,1]), quantile(aaa[,2],bbb[1,2]), quantile(aaa[,3],bbb[1,3])
            quantile(aaa[,1],bbb[2,1]), quantile(aaa[,2],bbb[2,2]), quantile(aaa[,3],bbb[2,3])
            quantile(aaa[,1],bbb[3,1]), quantile(aaa[,2],bbb[3,2]), quantile(aaa[,3],bbb[3,3])
            quantile(aaa[,1],bbb[4,1]), quantile(aaa[,2],bbb[4,2]), quantile(aaa[,3],bbb[4,3])
            quantile(aaa[,1],bbb[5,1]), quantile(aaa[,2],bbb[5,2]), quantile(aaa[,3],bbb[5,3])



Now if I only two vectors, it would be enough for me to define ccc=quantile(aaa,bbb). However, if I do this when aaa and bbb are matrix, quantile(aaa,bbb) does something else -- it gives the percentiles bbb of the whole set of matrix elements rather than considering separately the quantiles of the different columns.

I suspect I'll need to use "apply" in some form but have been able to come up with the correct form.

As you might have imagined, this arises in the  context of simulating random variables from different distribution in empirical form that are correlated through a copula.

Thanks in advance for your help!

Pietro
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