       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:= Subscript[\[Sigma]2, BD] :=
>  TransformedDistribution[((Subscript[n, obs] - 1)/df) Subscript[F,
>    BD], Subscript[F, BD] \[Distributed]
>    FRatioDistribution[Subscript[n, obs] - 1, df]]
>
> In:= Mean[Subscript[\[Sigma]2, BD]] /. df -> Subscript[n, obs] -
> 1
>
> Out= \!\(\*
> 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:= Mean[Subscript[\[Sigma]2, BD]] /. df -> Subscript[n, obs] +
> 1
>
> Out= Mean[
>  TransformedDistribution[(\[FormalX] (-1 + Subscript[n, obs]))/(
>   1 + Subscript[n, obs]), \[FormalX] \[Distributed]
>    FRatioDistribution[-1 + Subscript[n, obs], 1 + Subscript[n, obs]]]=
]

```

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