       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, 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}]

```

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