FullSimplify TransformedDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg120009] FullSimplify TransformedDistribution
- From: paulvonhippel at yahoo <paulvonhippel at yahoo.com>
- Date: Tue, 5 Jul 2011 05:10:49 -0400 (EDT)
Here's some behavior in Mathematica 8.0.0.0 that doesn't make sense to me. Using TransformedDistribution, I want to find the mean of a scaled F distribution. The answer depends on the argument df. When I replace df with n_obs - 1, I get a nice simplified answer. But when I replace df with n_obs + 1, the answer doesn't simplify. From hand calculations I know that the answers are equally simple. Why is Mathematica simplifying the first answer but not the second? I am aware I should upgrade to 8.0.1, but I'm not sure that will fix the problem. Input and output are pasted below -- I welcome suggestions about how to fomat the pasted output more cleanly. In[126]:= Subscript[\[Sigma]2, BD] := TransformedDistribution[((Subscript[n, obs] - 1)/df) Subscript[F, BD], Subscript[F, BD] \[Distributed] FRatioDistribution[Subscript[n, obs] - 1, df]] In[127]:= Mean[Subscript[\[Sigma]2, BD]] /. df -> Subscript[n, obs] - 1 Out[127]= \!\(\* TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ { FractionBox[ RowBox[{ RowBox[{"-", "1"}], "+", SubscriptBox["n", "obs"]}], RowBox[{ RowBox[{"-", "3"}], "+", SubscriptBox["n", "obs"]}]], RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", SubscriptBox["n", "obs"]}], ">", "2"}]}, {"Indeterminate", TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]\) In[128]:= Mean[Subscript[\[Sigma]2, BD]] /. df -> Subscript[n, obs] + 1 Out[128]= Mean[ TransformedDistribution[(\[FormalX] (-1 + Subscript[n, obs]))/( 1 + Subscript[n, obs]), \[FormalX] \[Distributed] FRatioDistribution[-1 + Subscript[n, obs], 1 + Subscript[n, obs]]]]