Multivariate mixture distributions

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Multivariate mixture distributions

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Hello, I am searching for a way to generate random values from a multivariate mixture distribution. For starters, one could create a mixture distribution consisting of a gamma or normal distribution and then a tail/spike of values in a normal distribution (eg as in Figure 1, A Eyre-Walker, PD Keightley. 2007. The distribution of fitness effects of new mutations. Nature Review Genetics 8: 610-618)
I am not certain how to implement this in the R environment. The implementation becomes even more difficult if one wants to generalize this distribution to multiple variables that are related to one another via some correlation structure. The analogous situation is a multivariate normal distribution with the shape given by the covariance matrix. 
What I need for my research program is to generate values for each of 3 random variables with ("one-dimensional") distributions as in Figure 1 and yet simultaneously choose a value for each variable so that the resolved values are correlated in some way (eg if a high value for variable 1 is chosen, it is likely that values 2 and 3 are low).
Thanks in advance for the help.
Patrick SoprovichBiology Department, Dalhousie University


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