Re: FullSimplify TransformedDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg120057] Re: FullSimplify TransformedDistribution
- From: paulvonhippel at yahoo <paulvonhippel at yahoo.com>
- Date: Thu, 7 Jul 2011 07:30:55 -0400 (EDT)
- References: <iuukl7$epn$1@smc.vnet.net>
Never mind. Figured it out. On Jul 5, 4:14 am, paulvonhippel at yahoo <paulvonhip... at yahoo.com> wrote: > 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]]]= ]