Understanding TransformedDistribution
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- Subject: [mg131893] Understanding TransformedDistribution
- From: "Ernst H.K. Stelzer" <ernst.stelzer at physikalischebiologie.de>
- Date: Mon, 28 Oct 2013 00:40:08 -0400 (EDT)
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Through a question on StackExchange I came to know TransformedDistribution, which allows me to sort of develop new distributions based on the ones defined in Mathematica. Instead of using my own functions, which work perfectly well, I now tried to repeat a number of older calculations using e.g. UniformDistribution.
When I combine two via
TransformedDistribution[2 (x - 4/5 y), {x \[Distributed] UniformDistribution[{-1, 1}], y \[Distributed] UniformDistribution[{-(4/5), 4/5}]}]
to generate a kind of annular function and then look at the PDF, I get
PDF[%, x]
\[Piecewise] 1/4 -(18/25)<=x<=18/25
1/256 (82-25 x) 18/25<x<82/25
1/256 (82+25 x) -(82/25)<x<-(18/25)
0 True
However, I expect, what I get when I enter
2 (PDF[UniformDistribution[{-1, 1}], x] -
4/5 PDF[UniformDistribution[{-(4/5), 4/5}], x])
2 ((\[Piecewise] 1/2 -1<=x<=1
0 True
)-4/5 (\[Piecewise] 5/8 -(4/5)<=x<=4/5
0 True
))
Does anybody have a clue which mistake I made?
Greetings
Ernst
Prof. Dr. Ernst H.K. Stelzer, Physical Biology (FB 15, IZN)
Buchmann Institute for Molecular Life Sciences (BMLS, CEF-MC)
Goethe Universit=E4t Frankfurt am Main (Campus Riedberg)
Max-von-Laue-Strasse 15, D-60438 Frankfurt am Main, Germany
Tel +49 (69) 798 42547, x42545 (Michaela Koller)
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ernst.stelzer at physikalischebiologie.de
stelzer at bio.uni-frankfurt.de
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