Re: Area Under Curve (Min Length Interval)
- To: mathgroup at smc.vnet.net
- Subject: [mg53909] Re: [mg53889] Area Under Curve (Min Length Interval)
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Fri, 4 Feb 2005 04:11:03 -0500 (EST)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
The minimum interval requires PDF[dist, a] == PDF[dist, b] Needs["Statistics`"]; Needs["Graphics`"]; minimumInterval[dist_, area_?NumericQ] := Module[{a,b,mu=Mean[dist],ae,be}, ae=Max[mu/4,Domain[dist][[1,1]]]; be=Min[2*mu,Domain[dist][[1,2]]]; {a,b} /. FindRoot[{ PDF[dist,a]==PDF[dist,b], CDF[dist,b]-CDF[dist,a]==area}, {a,ae},{b,be}]]; dist=ChiSquareDistribution[5]; {a,b}= minimumInterval[dist,0.93] {0.37253,10.3441} FilledPlot[ {0,UnitStep[x-a]-UnitStep[x-b],1}* PDF[dist,x],{x, Max[a-3,Domain[dist][[1,1]]], Min[b+3,Domain[dist][[1,2]]]}, PlotPoints->50]; Bob Hanlon > > From: Bruce Colletti <vze269bv at verizon.net> To: mathgroup at smc.vnet.net > Date: 2005/02/02 Wed AM 06:25:53 EST > Subject: [mg53909] [mg53889] Area Under Curve (Min Length Interval) > > Re Mathematica 5.1. > > How would I compute the minimum length interval over which the area under f(x) is given? > > For instance, as shown below, f(x) is the PDF of a chi-square distributed random variable whose CDF is F[x]. Seeking the minimum length 93%- interval [a,b], the code returns "Obtained solution does not satisfy the following constraints within Tolerance -> 0.001..." Fiddling with options has been futile. > > Any ideas? Thankx. > > Bruce > > F[x_] := CDF[ChiSquareDistribution[5], x] > > Minimize[{b - a, F[b] - F[a] == 0.93, b > a > 0}, {a, b}] > > NMinimize[{b - a, F[b] - F[a] == 0.93, b > a > 0}, {a, b}] > > >