> However, my variable is simulated from the cumulative distribution function
> of the Poisson distribution. 
Then I am afraid I don't know what you're trying to achieve. 
Or why.

However, the principle holds; write a function that maps [0,1] to the 'pattern' 
you want, do that and apply it to the result from randomLHS. 
It happens that for generating data that follow a given probability 
distribution F, that function is the quantile function for F so you often do 
not need to write it.


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