Latin Hypercube Sampling (LHS) with non-normal and non-uniform random variables

Dear all,

I am having some problems defining a latin hypercube sampling technique to run my simulations and I am wondering if you may give me a hand.

Consider four random variables, X1, X2, X3 and X4, with the following statistical features:

X1~Normal (Mean=330, StDev=33),

X2~Normal (Mean=0,StDev=1/1000),

X3~Lognormal (Mean=1.5, StDev=0.075),

X4~ExtTypeI(Mean=10, StDev=2.5),

To obtain convergence, I estimate that I would need 300 simulations sampled with LHS technique (opposed to 10000+ with direct Monte-Carlo technique) but I have no idea how to go about it. I know that I need to:

(i) somehow split each random variable distribution in 300 intervals of equal probability,

(ii) randomly generate a number within the range of each interval and

(iii) finally combine the random variables considering each interval only once. By other words, labelling Xi (j) as the random value of the variable i for the interval j, the result would be something like:

X1 (251) + X2 (12) + X3 (47) + X4 (19)

X1 (77) + X2 (199) + X3 (229) + X4 (55)

…

So on, until 300th combination.

Any ideas?

Regards,

F.