       Re: Plot InverseSurvivalFunction

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• Subject: [mg132018] Re: Plot InverseSurvivalFunction
• From: "Eduardo M. A. M. Mendes" <emammendes at gmail.com>
• Date: Sun, 17 Nov 2013 18:21:55 -0500 (EST)
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```Hello

Yes, it is faster.  Many thanks.

The last command should be Plot[invsurv[q], {q, 0.01, 0.999}], shouldn't it?

Cheers

Ed

On Nov 15, 2013, at 10:22 PM, Itai Seggev <itais at wolfram.com> wrote:

> On Fri, Nov 15, 2013 at 06:41:57AM -0500, Eduardo M. A. M. Mendes wrote:
>> Hello
>>
>> Is there any way to evaluate (or even plot) the inverse survival function of a sum of two Fs?
>>
>> Here is what I have so far
>>
>> \[ScriptCapitalD]=TransformedDistribution[u+v,{u\[Distributed]FRatioDistribution[2,2 2],v\[Distributed]FRatioDistribution[2,2 2]}]
>>
>> PDF[\[ScriptCapitalD],x]
>>
>> Plot[PDF[\[ScriptCapitalD],x],{x,0,10},Filling->Axis]
>>
>> CDF[\[ScriptCapitalD],x]
>>
>> Plot[CDF[\[ScriptCapitalD],x],{x,0,10},Filling->Axis]
>>
>> All above commands return the results I expect but when I try
>>
>>
Plot[InverseSurvivalFunction[\[ScriptCapitalD],x],{x,0,1},Filling->Axis,PlotRange-> Full]
>>
>> Mathematica won't show any curve. Does it mean that Mathematica could not find an expression for it?
>>
>> I know that the sum of Fs will get rather complicated.
>>
>> Is there any way to get an output from InverseSurvivalFunction[\[ScriptCapitalD],0.95] for instance?
>>
>
> There appears to be a bug that InverseSurivivalFunction doesn't evaluate when
> given a TransformedDistribution.  One trick to deal with that is to create a
> new distribution from the PDF of the TransformedDistribution:
>
> \[ScriptCapitalD] =
>  ProbabilityDistribution[
>   PDF[TransformedDistribution[
>     u + v, {u \[Distributed] FRatioDistribution[2, 2 2],
>      v \[Distributed] FRatioDistribution[2, 2 2]}], x], {x,
>    0, \[Infinity]}];
>
>
> In:= InverseSurvivalFunction[\[ScriptCapitalD], 0.5]
>
> Out= 2.25061
>
> However, this function will be extremely slow and not really usable for
> plotting.  I tried plotting it out of curiousity to see the timing, and when I
> didn't finish after 7 minutes or so I gave up.  On the other hand, it will be
> usable if you need to evaluate a small number of points with relative accuracy.
>
> For plotting, you could do something like the following:
>
> survival[z_] =
> SurvivalFunction[
>  TransformedDistribution[
>   u + v, {u \[Distributed] FRatioDistribution[2, 2 2],
>    v \[Distributed] FRatioDistribution[2, 2 2]}], z]
>
> invsurv[q_Real] :=
> Block[{z}, z /. FindRoot[survival[z] == q, {z, 1}]]
>
> Plot[qun[q], {q, 0.01, 0.999}]
>
> Which would still not be lightning fast but usable (something like 15 seconds
> on my machine.)
>
>> Many thanks
>>
>> Ed
>>
>>
> --
> Itai Seggev
> Mathematica Algorithms R&D
> 217-398-0700

```

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