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Re: Plot InverseSurvivalFunction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132013] Re: Plot InverseSurvivalFunction
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Fri, 15 Nov 2013 18:36:44 -0500 (EST)
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  • References: <20131115114157.A96816A4F@smc.vnet.net>

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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