Re: Plot InverseSurvivalFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg132016] Re: Plot InverseSurvivalFunction
• From: "Eduardo M. A. M. Mendes" <emammendes at gmail.com>
• Date: Sun, 17 Nov 2013 18:21:15 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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• References: <20131115114157.A96816A4F@smc.vnet.net> <CAEtRDScEf8=PeTHu_ZwmOZ11JX0Qgofe9KJc_J0gzUgyhTteAw@mail.gmail.com>

```Many many thanks

Ed

On Nov 15, 2013, at 5:36 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote:

> I recommend that you estimate it using an interpolation function
>
> \[ScriptCapitalD] = TransformedDistribution[u + v,
>     {Distributed[u, FRatioDistribution[2, 2*2]],
>      Distributed[v, FRatioDistribution[2, 2*2]]}];
>
> Plot[Evaluate[SurvivalFunction[\[ScriptCapitalD],x]],
> {x,0,10},Filling->Axis]
>
> survFunc[x_]=Evaluate[SurvivalFunction[\[ScriptCapitalD],x]]
>
> Piecewise[{{1, x <= 0}},
>   1 - (x*(192 + 304*x + 120*x^2 + 18*x^3 + x^4) -
>      192*(2 + x)*Log[(2 + x)/2])/((2 + x)*(4 + x)^4)]
>
> invSurvFuncEst=Interpolation[Reverse/@
> Table[{x,survFunc[x]},{x,0,10,0.005}]];
>
> (invSurvFuncEst/@(survFunc/@Range[0,10,0.005]))==
> Range[0,10,0.005]
>
> True
>
> Plot[invSurvFuncEst[q],{q,survFunc[10],1},
> AxesOrigin->{0,0},Filling->Axis]
>
> invSurvFuncEst[0.95]
>
> 0.37722527322144106
>
> Evaluate[SurvivalFunction[\[ScriptCapitalD],x]]/.x->%
>
> 0.949999999642922
>
>
> Bob Hanlon
>

```

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