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Let $X$ be Laplace distributed with mean $\mu_L$ and scale parameter $\lambda$, and $Y$ be Gaussian distributed with mean $\mu_G$ and standard deviation $\sigma$.

Is there a name for the probability distribution describing the variable $Z=X+Y$?

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I don't think so. You tried googling? –  dineshdileep Jan 11 '13 at 6:27
    
I'm pretty sure there's not. –  Jonathan Christensen Jan 11 '13 at 18:08
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