Sum of Correlated Exponential RVs

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Hi All :)

say Y = X1 + X2+ X3, where X1, X2 and X3 are each exponentially distributed RV. This makes Y also a RV. If X1 and X2 and X3 are independent, the pdf of Y can be found by the convolution of the individual pdfs.

What if X1, X2 and X3 are correlated? How do we go about finding the pdf of Y?

many thanks in advance

:-p
 
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1. Simulate,
2. Fit a polynomial to simulation data.

Makarov, G. (1981) "Estimates for the distribution function of a sum of two random variables when the marginal distributions are fixed," Theory of Probability and its Applications, 26, 803-806.

See others under References in:
http://www.math.ethz.ch/%7Estrauman/preprints/pitfalls.pdf

Also see:
http://www.merl.com/publications/TR2006-010/
http://ieeexplore.ieee.org/Xplore/l...29369/01327853.pdf?isnumber=&arnumber=1327853
http://arxiv.org/abs/cond-mat/0601189
 
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