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Re: Plot InverseSurvivalFunction
Posted:
Nov 17, 2013 4:23 AM


Hello
Many thanks for the clearing several points and for the alternative functions to plot the survival function.
Cheers
Ed
On Nov 15, 2013, at 9:36 PM, Bill Rowe <readnews@sbcglobal.net> wrote:
> On 11/15/13 at 6:41 AM, emammendes@gmail.com (Eduardo M. A. M. > Mendes) wrote: > >> 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? > > When you say Mathematica didn't show a curve exactly what do you > mean? Do you mean you got the result > > Plot[I, {x, 0, 1}] > > will give, i.e., a graphic showing an axis with no curve? Or do > you mean simply you didn't get anything in the time you were > willing to wait? > > If it is the latter, then there is a way to get the desired > plot. First, note the difference in the amount of time to > produce a plot between > > d = TransformedDistribution[ > u + v, {u \[Distributed] FRatioDistribution[2, 2 2], > v \[Distributed] FRatioDistribution[2, 2 2]}]; > > pdf = PDF[d, x]; > Plot[pdf, {x, 0, 10}, Filling > Axis] > > and > > Plot[PDF[d, x], {x, 0, 10}, Filling > Axis] > > When you do Plot[PDF[d,x] ... Mathematica substitutes a > numerical value for x then finds the density function of your > distribution with that value. That is, Mathematica repeats the > computation of the density function for every numerical value > used for x. > > By doing pdf=PDF[d,x];Plot[pdf ... the computation of the > density function is done once rather than many times. This way, > Mathematica does far less computation and gets the end result > much faster. > > Now, this won't completely solve the problem since > > InverseSurvivalFunction[d, x] > > returns unevaluated which means Mathematica will have to do a > lot of computation to make a plot with > > Plot[InverseSurvivalFunction[d,x], ... > > But notice > > SurvivalFunction[d,x] does evaluate to closed form expression. > So, a quick way to get the desired plot would be: > > sf = SurvivalFunction[d, x]; > ParametricPlot[{sf, x}, {x, 0, 10}, AspectRatio > 1/GoldenRatio] > > >



