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>