Re: Area Under Curve (Min Length Interval)

*To*: mathgroup at smc.vnet.net*Subject*: [mg53900] Re: [mg53889] Area Under Curve (Min Length Interval)*From*: Chris Chiasson <chris.chiasson at gmail.com>*Date*: Wed, 2 Feb 2005 18:10:41 -0500 (EST)*References*: <200502021125.GAA28978@smc.vnet.net>*Reply-to*: Chris Chiasson <chris.chiasson at gmail.com>*Sender*: owner-wri-mathgroup at wolfram.com

I think Bruce's code would usually work, but Minimize isn't able to pick up on what is happening or what you want; I'm not sure which. Anyway, here are a few lines of code that graphically demonstrate what is happening and give the (locally) correct solution. << Statistics`ContinuousDistributions` F[x_] = CDF[ChiSquareDistribution[5], x]; NMinimize[{b - a, F[b] - F[a] == 93/100, b > a > 0}, {a, b}] tempsoln = Solve[F[b] - F[a] == 93/100, b][[1, 1]] intersectingsurfaces = Plot3D[#, {a, 0, 2}, {b, 0, 40}, AxesLabel -> {"a", "b", "c"}, DisplayFunction -> Identity] & /@ {F[b] - F[a], 0.93} Show[intersectingsurfaces, ViewPoint -> {0, 0, 1}, DisplayFunction -> $DisplayFunction] Plot[Evaluate[b /. tempsoln], {a, 0, 1.3}, AxesLabel -> {"a", "b"}] Plot[Evaluate[b - a /. tempsoln], {a, 0, 1.3}, AxesLabel -> {"a", "b-a"}] NMinimize[{b - a /. tempsoln, b > a > 0}, {a, b}] For clarity, these commands may be evaluated one at a time. Regards, On Wed, 2 Feb 2005 06:25:53 -0500 (EST), Bruce Colletti <vze269bv at verizon.net> wrote: > 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}] > > -- Chris Chiasson Kettering University Mechanical Engineering Graduate Student 1 810 265 3161

**Follow-Ups**:**Re: Re: Area Under Curve (Min Length Interval)***From:*DrBob <drbob@bigfoot.com>

**References**:**Area Under Curve (Min Length Interval)***From:*Bruce Colletti <vze269bv@verizon.net>