Area Under Curve (Min Length Interval)
- To: mathgroup at smc.vnet.net
- Subject: [mg53889] Area Under Curve (Min Length Interval)
- From: Bruce Colletti <vze269bv at verizon.net>
- Date: Wed, 2 Feb 2005 06:25:53 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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}]
- Follow-Ups:
- Re: Area Under Curve (Min Length Interval)
- From: Chris Chiasson <chris.chiasson@gmail.com>
- Re: Area Under Curve (Min Length Interval)