Latin hypercube sampling of correlated paramters with different distributions?

Hi everbody,

For my PhD I'm doing probabilistic simulations. I have 5 input parameters, IP1-5. IP1, IP2,IP3,IP4 are normaly distributed, IP5 is log normaly distributed, the mean and SD (Variation coeficient*mean) of each parameter is known. So random sampling of the parameters based on its distribution and combining them randomly is no problem.

Now I use this code for that: (VCC is the variation coeficient)

%Latin hypercube sampling

IP1=lhsnorm(IP1,IP1*VCC,1);
IP2=lhsnorm(IP2,IP2*VCC,1);    
IP3=lhsnorm(IP3,IP3*VCC,1);   
                while IP3<0
                IP3=lhsnorm(IP3(1,b),IP3(1,b)*VCC,1); 
                end
IP4=lhsnorm(IP4,IP4*VCC,1);   
                while IP4<0
                IP4=lhsnorm(IP4,IP4*VCC,1); 
                end
IP5=lhsnorm(log(IP5),log(IP5)*VCC,1);

But I know there is a cetrain correlation between my paramters from other researchers(See table in attachment).

Can anyone help me to make sure that my sampling combinations have the same correlation as in the table? Otherwise I will sample a lot of data which is not representative for reality. I don't find a way to make my correlation and my sampling interact in a good way. In my opion it would be best to first do the sampling randomly for example for 3000 samples and afterwards order them that they fit the correlation as good as possible. Because when I would redo the sampling if the sample is not fitting the correlation coefficients, I think my distributions will not be correct anymore as more extreme values in the tales will be more difficult to correlate with the other parameters.

Can anyone help me with this?

Many thanks in advance!