# Sum of Correlated Exponential RVs

1. Jul 20, 2007

### tpkay

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?

:tongue2:

2. Jul 21, 2007

### EnumaElish

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/~strauman/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

Last edited: Jul 21, 2007