more problems with TransformedDistribution

• To: mathgroup at smc.vnet.net
• Subject: [mg120707] more problems with TransformedDistribution
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 6 Aug 2011 02:12:11 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```I don't understand this behaviour. Consider:

D1 =
TransformedDistribution[{u, v + 1}, {u \[Distributed] UniformDistribution[{0, 1}],  v \[Distributed] UniformDistribution[{0, 1}]}];

RandomVariate[D1, {3}]

{{0.7615750941433532, 1.3679530660935457},
{0.244892942700228, 1.060960354163685},
{0.7802933339717009, 1.5833190582890353}}

Fine, as expected. Next:

D2 =
TransformedDistribution[{u, v^2}, {u \[Distributed] UniformDistribution[{0, 1}], v \[Distributed] UniformDistribution[{0, 1}]}];

RandomVariate[D2, {3}]

{{0.06686173309743126, 0.21489944889140244},
{0.38263698808007707, 0.45277199160209924},
{0.07060737924762184, 0.10567112037126829}}

Again fine. Now let's try a simple product:

D3 = TransformedDistribution[{u,v}, {u \[Distributed] UniformDistribution[{0, 1}], v \[Distributed] UniformDistribution[{0, 1}]}];

RandomVariate[D3, {3}]

RandomVariate[TransformedDistribution[{\[FormalX]1,\[FormalX]2},{\[FormalX]1\[Distributed]UniformDistribution[{0,1}],\[FormalX]2\[Distributed]UniformDistribution[{0,1}]}],{3}]

Doesn't work. Why?

(Of course one I can get the answer using ProductDistribution etc. but that is not the point ....)

Andrzej Kozlowski

```

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