Understanding TransformedDistribution

• To: mathgroup at smc.vnet.net
• 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

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stelzer at bio.uni-frankfurt.de

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