Closed form for convolutions of random variables

Question

Is it possible to get Mathematica (9) to calculate PDF's for combined distributions? I can't seem to find the right notation, if this is possible at all. My attempts:

PDF[NormalDistribution[0, 1] + NormalDistribution[0, 1], x]

Nor can we store a distribution to a variable:

z \[Distributed] NormalDistribution[0, 1]
PDF[z, x]

score 5 · Accepted Answer · edited Mar 13 '13 at 19:59

5

dist = TransformedDistribution[u + v, 
 {u \[Distributed] NormalDistribution[μ1, σ1], 
  v \[Distributed] NormalDistribution[μ2, σ2]}];
PDF[dist, x]

enter image description here

Note: check the correct syntax for PDF in the docs.

edited Mar 13 '13 at 19:59

Sjoerd C. de Vries

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answered Mar 13 '13 at 17:49

kglr

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@Matt, my pleasure. Welcome to Mathematica.SE. – kglr Mar 13 '13 at 18:02
Thanks for the welcome! I do most of my coding in R, working on a review of Mathematica for R users right now... – Matt Asher Mar 13 '13 at 18:12
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@MattAsher I suppose you're aware of Mathematica 9's new RLink feature, right? – Sjoerd C. de Vries Mar 13 '13 at 19:58
@Sjoerd C. de Vries Yes I am. I'll be evaluating some of RLink's capabilities in my review. – Matt Asher Mar 15 '13 at 16:40

Closed form for convolutions of random variables

1 Answers1