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I have a random variable X that is a mixture of a binomial and two normals (see what the probability density function would look like (first chart))
and I have another random variable Y of similar shape but with different values for each normally distributed side.

X and Y are also correlated, here's an example of data that could be plausible :

    X     Y 1.  0    -20 2. -5     2 3. -30    6 4.  7    -2 5.  7     2 

As you can see, that was simply to represent that my random variables are either a small positive (often) or a large negative (rare) and have a certain covariance.

My problem is : I would like to be able to sample correlated and random values from these two distributions.

I could use Cholesky decomposition for generating correlated normally distributed random variables, but the random variables we are talking here are not normal but rather a mixture of a binomial and two normals.

Many thanks!

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    is the same bernoulli trial used to generate X and Y - or are they different? and if the latter - are they also correlated in some way?2010-12-17
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    @ronaf No it is not the same bernoulli trial. Each variable has a different % to choose between 2 normal distribution (of course for each variable, these % equal to 1 but it might be 80-20 or 70-30, etc.) I would say that each's variable bernoulli trial are not correlated but maybe I am wrong...I am not sure because can't we say that 'everything' is correlated somehow? How could I be sure if they are correlated or not? Kind regards2010-12-17
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    Seeing that there is no more answers and comments, I suggest moving this question to stats.stackexchange.com2010-12-20

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