Simplifying TransformedDistribution

• To: mathgroup at smc.vnet.net
• Subject: [mg120726] Simplifying TransformedDistribution
• From: Paul von Hippel <paulvonhippel at yahoo.com>
• Date: Sun, 7 Aug 2011 06:16:47 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201108060612.CAA13002@smc.vnet.net> <21F4E2DB-98AB-490F-ABBC-12C19828590F@mimuw.edu.pl>
• Reply-to: Paul von Hippel <paulvonhippel at yahoo.com>

```Under what circumstances will the TransformedDistribution function simplify the distribution given by a user? Is there a way to force further simplification? For example, below, both In[78] and In[79] can be simplified to the same student's t distribution -- yet TransformedDistribution simplifies only In[78]. Is there a way to get In[79]simplified as well?

In[78]:= TransformedDistribution[
Z/Sqrt[U/v], {Z \[Distributed] NormalDistribution[0, Sqrt[2]],
U \[Distributed] ChiSquareDistribution[v]}]

Out[78]= StudentTDistribution[0, Sqrt[2], v]

In[79]:= TransformedDistribution[(Z1 + Z2)/
Sqrt[U/v], {Z1 \[Distributed] NormalDistribution[0, 1],
Z2 \[Distributed] NormalDistribution[0, 1],
U \[Distributed] ChiSquareDistribution[v]}] // FullSimplify

Out[79]= TransformedDistribution[(\[FormalX]1 + \[FormalX]2)/Sqrt[\
\[FormalX]3/v], {\[FormalX]1 \[Distributed]
NormalDistribution[0, 1], \[FormalX]2 \[Distributed]
NormalDistribution[0, 1], \[FormalX]3 \[Distributed]
ChiSquareDistribution[v]}]

```

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